Mid-Year Virtual Conference Schedule
SMB Math-Epidemiology/Math-Immunology Subgroups Mid-Year Mini Virtual Conference
February 27-28, 2022
Theme: "Epidemiology meets Immunology and Vice Versa - Linking Math Epidemiology to Math Immunology”
NOTE: All times are in Eastern Time (New York Time)
Zoom Link for ALL Talks (Contributed and Keynote): https://lehigh.zoom.us/j/97499190204
Meeting ID: 974 9919 0204
Zoom Link (Webinar) for Panels: Debate and Session to Honor Prof. Brauer: https://lehigh.zoom.us/j/93652555826
Meeting ID: 93652555826
Sunday, February 27, 2022
9:00 – 11:50 AM
Contributed talks (7 Talks - 20 minutes + 4 minutes question and Speaker Change)
Session Chair: Aurélie Akossi
Md Rafiul Islam, Iowa State University, USA
Accounting for ethnicity improves outcomes associated with COVID-19 vaccine prioritization strategies
In the United States people of the same ethnic group are much more likely to interact with people of the same ethnic group—a phenomenon known as ethnic homophily. Moreover, ethnicities of lower average socio-economic status are known to hold proportionately more low- income jobs with more contacts and are thus more at risk of virus infection. When developing a strategy prioritizing population groups for vaccination, taking ethnicity into account could therefore provide better outcomes (e.g., fewer deaths, cases, etc.). In this study, we modified a detailed compartmental COVID-19 disease model we recently developed to investigate the optimal vaccine allocation strategy for a population stratified by age, ethnicity, occupation type (low versus high virus exposure) and pre-existing health con- ditions. Given limited vaccine availability at the beginning of the roll-out, a greedy algorithm determined iteratively which sub-population should receive the next few available vaccines, based on different outcome metrics such as minimizing deaths, cases, or years of life lost (YLL). Taking ethnicity into account led to generally better outcomes. Moreover, the “continuous”, greedy approach, which may be hard to implement in practice, outperformed phase-based allocation strategies where certain sub-populations are fully vaccinated (except for hesitant individuals) before other sub-populations get access. Our research suggests that future vaccine prioritization strategies, for COVID-19 variants or other infectious diseases, may be improved by accounting for ethnicity in the roll-out.
Loreniel E. Anonuevo, University of the Philippines Mindanao - AMDABIDSS-Health
Modeling the COVID-19 dynamics in Davao City, Philippines under different variants-of-concern
Loreniel E. Añonuevo1*, Rey Audie S. Escosio1,2, El Veena Grace A. Rosero3, Jayve Iay E. Lato1, Deza A. Amistas1, Zython Paul T. Lachica1 , Alexis Erich S. Almocera1,3, Jayrold P. Arcede1,4, May Anne E. Mata1,3 *
1Center for Applied Modeling Data, Analytics, and Bioinformatics for Decision Support Systems in Health, University of the Philippines Mindanao, Davao City, Philippines; 2Institute of Mathematics, University of the Philippines Diliman, Quezon City, Philippines; 3Department of Mathematics, Physics, and Computer Science, University of the Philippines Mindanao, Davao City, Philippines; 4Department of Mathematics, Caraga State University, Butuan City, Philippines
Being the Philippines’ largest city, Davao City is subject to widespread transmission and risks caused by the various COVID-19 variants-of-concern (VOCs). We modeled the COVID-19 transmission dynamics and estimated the model parameters with respect to the detection of COVID-19 VOCs in Davao City, Philippines. Specifically, we used a modified Susceptible- Exposed-Infectious-Recovered (SEIR) compartmental model and performed a piecewise parameter estimation using Latin Hypercube Sampling and bootstrapping techniques to investigate the dynamics of the pathogen before and after the detection of each new VOC. Key epidemiological parameters and the time-varying reproduction number were examined to capture the relative effects of the VOCs towards the COVID-19 surges in Davao City. The collected data showed that the first positive cases of the alpha and beta variants were detected only four days apart and there was a delay in the variants’ effect to the pathogen’s transmission. There were 42 days of lag effect on alpha and beta variants, 70 days for delta, and 28 days for the omicron variant. The alpha and beta variants had the fastest transmission rate but its positivity rate was the lowest among VOC. The delta variant had the lowest transmission rate but it had a high positivity rate. The omicron had a faster transmission rate than delta and had the highest positivity rate among VOC. As an effect of vaccine-induced immunity, it also had the highest proportion of mild and asymptomatic cases among variants. Results suggest a possibility of a massive number of unreported cases at large, especially that the omicron was detected to have spread during the holiday season. Policies on mass testing, isolation, vaccination among other interventions have to be reviewed to curb the further spread of the virus.* Corresponding author. E-mail: leanonuevo@carsu.edu.ph and memata@up.edu.ph
Md Shahriar Mahmud, State University of Bangladesh, Bangladesh
SARS-CoV-2 pandemic in Bangladesh: A study on the host population & Rohingya population
M. Kamrujjaman, M.S. Mahmud∗, S. Ahmed, M.O. Qayum, M.M. Alam, M.N. Hassan, M.R. Islam, K.F. Nipa & U. Bulut
Bangladesh, a country with 164.7 million population, hosts more than 0.8 million Rohingya refugees from Myanmar. The low health immunity, lifestyle, lim- ited access to good healthcare and social-security services cause this population to be at high risk of far more direct effects of COVID-19 than the host population. Therefore, evidence-based forecasting of the COVID-19 burden is vital in this regard. In this study, we aimed to forecast the COVID-19 obligation among the host and Rohingya population of Bangladesh to keep up with the disease outbreak’s pace, health needs, and disaster preparedness. To estimate the possible consequences of COVID-19 in Bangladesh, we used a modified Susceptible-Exposed-Infectious-Recovered (SEIR) transmission model. All of the values of different parameters used in this model were from the Bangladesh Government’s database and the relevant emerging literature. We addressed two different scenarios, i.e., the best-fitting model and the good-fitting model with unique consequences of COVID-19. Our best fitting model suggests that there will be reasonable control over the transmission of the COVID-19 disease. At the end of December 2020, there has been only 169 confirmed COVID-19 cases in the Rohingya refugee camps. The average basic reproduction number (R0) had been successfully esti- mated to be 0.7563. Our analysis suggests that, due to the extensive precautions from the Bangladesh government and other humanitarian organizations, the coronavirus disease will be under control if the maintenance continues like this. However, detailed and prag- matic preparedness should be adopted for the worst scenario.
Sarita Bugalia, Central University of Rajasthan, India
Mathematical modeling of intervention and low medical resource availability with delays: Applications to COVID-19 outbreaks in Spain and Italy
Sarita Bugalia∗1, Jai Prakash Tripathi1, Hao Wang2
1Department of Mathematics, Central University of Rajasthan, Bandar Sindri, Kishangarh-305817, Ajmer, Rajasthan, India
2 Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton AB T6G 2G1, Canada
saritabugalia44@gmail.com (*presenter)
Infectious diseases have been major causes of death, and millions of people die every year from contagious diseases. Mathematical models have played a significant role in understanding the spread mechanism and control of contagious diseases in the past few decades. In this paper, we propose a delayed SEIR epi demic model with infectious force under intervention strategies and recovery/treatment rates under the low availability of resources. We put our efforts to understand the impact of intervention strategies and available resources for treatment in the spread of diseases. We study the non-delayed model and delayed model separately and based on the basic reproduction number (R0); it is revealed that both model systems ex hibit two equilibria, namely, the disease-free equilibrium and the endemic equilibrium. For the non-delayed model, stability analysis for both disease-free and endemic equilibriums are performed. When R0 = 1, the non-delayed system undergoes a transcritical bifurcation. Further, we incorporate two-time delays; the first time delay τ1 represents the latent period of the intervention strategies and the second time delay τ2 due to the period that is used to cure the infected individuals. For delayed system, local stability of disease-free equilibrium is performed with τ1 > 0, τ2 > 0, when R0 < 1. If R0 > 1, threshold values of both delay pa rameters for the local stability of endemic equilibrium have been obtained. It has been investigated that the incorporation of two-time delays changes the dynamics of the system via Hopf-bifurcation and oscillations. The direction and stability of delay induced Hopf-bifurcation have also been established using normal form theory and center manifold theorem. Furthermore, we also establish that the local Hopf bifurcation implies the global Hopf bifurcation. The length of delay has been estimated to preserve stability. Taking care of analytical outcomes, various numerical simulations have also been carried out to gain a deep understanding about the systems dynamics. Our results via numerical simulation demonstrate that by implementing more interventions, the infection level can be reduced, and the level of infection increases with the limitation of treatment. It has been shown that timely implementation of intervention strategies may be effective in con trolling the outbreak of the disease. Further, our study also suggests that to control and predict the disease spread, we should trim the time delays. Interestingly, we have parameterized the model system with the data of COVID-19 in Spain and Italy.
Lihong Zhao, University of California, Merced, USA
Assessing Re-opening Strategies for Mitigating COVID-19 Transmission on College Campuses
The COVID-19 pandemic has forced nearly every higher-education institute in the United States to transition all courses from face-to-face instruction to online or hybrid instruction in March 2020. At the same time, non-pharmaceutical interventions (NPIs) such as mask use in public and social distancing were implemented to “flatten the epidemic curve.” In this talk, I will introduce the mathematical model we use to investigate the effectiveness of various NPIs on controlling the spread of COVID-19 on UC Merced campus and present the global sensitivity analysis of model behavior. The results of this model were used to inform administration regarding decisions on scheduling and housing constraints for both Fall 2020 and Spring 2021 at UC Merced.
Prashant Kumar Srivastava, Indian Institute of Technology Patna, UK
Nonlinear Dynamical Behaviour of an Infectious Disease Model: Effect of Information, Saturated Treatment and Incubation delay
Tanuja Das, Prashant Kumar Srivastava*
Indian Institute of Technology Patna, 801106-India
*pksri@iitp.ac.in (Presenting Author)
When an infectious disease spreads in a population the information about disease prevalence also spreads. This causes the healthy individuals to change their behavior and therefore, the rate of infection is affected. Hence the incidence term in the model need to be appropriately modified to reflect this impact. Further, limitation of medical resources also has its impact on the dynamics of the disease. In this work, we propose and analyze a mathematical model which accounts for the information induced non-monotonic incidence function and saturated treatment function. The model analysis is carried out and it is found that due to nonlinear functions present in the model system, a rich and complex dynamics is exhibited by the model system. When R0 is below one, the disease may or may not die out due to the saturated treatment and a backward bifurcation may exist. Further, we also observe that disease eradication is possible if the medical resources are available for all. When R0 exceeds one, the existence of multiple endemic equilibria is observed. We find that model shows various bifurcations, oscillatory behavior hysteresis. We conclude that the limitation of medical resources may cause bi (multi) -stability and the effect of information plays significant role and gives rise to a rich and complex dynamical behaviour. Further, a delay SIR model considering the delay in incubation is proposed and analyzed. The non-monotonic incidence function and a saturated treatment function is considered as earlier. We obtain a threshold for disease persistence in the population. The model system shows the possibility of multiple endemic equilibria. We analytically study the stability of endemic equilibrium, when it is unique. This stability of the unique endemic equilibrium depends on the delay parameter and is found to be locally asymptotically stable conditionally along with the existence of Hopf bifurcation. Numerically, we observe stability switch of unique endemic equilibrium and existence of endemic bubble due to change in delay parameter. Further, we observe that bi-stable endemic equilibria in absence of delay can be transformed to oscillatory bi-stable limit cycles in presence of delay (when the delay is sufficiently large). Here the delay causes the change in stability of both the equilibria by generating two local Hopf bifurcations around both the equilibria which were stable in absence of delay. On the basis of above, we conclude that the non-monotonic incidence, saturated treatment and incubation delay play a crucial role in the dynamics of a disease and can exhibit very complex dynamical behavior which includes various kinds of bifurcations. Some of our observations are novel and are not explored much in the existing disease models.
Peter Rashkov, Institute of Mathematics and Informatics, Sofia, Bulgaria
How much complexity is needed to model epidemic patterns of dengue
Institute of Mathematics and Informatics, Sofia, Bulgaria
p.rashkov@math.bas.bg
Dengue fever is a vector-borne disease characterised by a cocirculation of multiple variants of the pathogen (dengue virus DENV1-DENV4). Mathematical modelling of dengue faces the challenges of finding a balance between accurate description of the disease dynamics, the different scales of modelling, and the associated levels of complexity which allow for establishing tractable causal relationships. One approach in dengue modelling is to use host-only models that include the vector dynamics implicitly, based on a quasi-steady state approximation in order to reduce complexity. However, these models are not directly suited for studies of intervention measures such as pest control or personal protec tion via repellents, which may influence the mosquito dynamics in a nonlinear fashion. We discuss some issues which emerge repeatedly in the mathematical models of dengue: differences in structure (host-only vs. host-vector models) and the effect on dynamic behaviour, the theoretical rationale that allows complexity reduction via time-scale separation, and ecological effects due to seasonal changes in the vector population. Numerical bifurcation analysis is used to compare the bifurcation structure of a host-vector model of two-strain dengue with reinfection to that of previous two-strain host-only models.
11:50 - 12:25 PM
Lunch Break
12:25 - 12:35 PM
Official Opening Remarks
12:35 - 1:25 PM
Keynote Address 1 (Introduction: Julie Spencer)
Dr. Stanca M. Ciupe, PhD, Professor, Department of Mathematics, Virginia Tech.
The role of testing in COVID-19 control
Abstract: Vaccination is considered the best strategy for limiting and eliminating the COVID-19 pandemic. The success of this strategy relies on the rate of vaccine deployment and acceptance across the globe. As these efforts are being conducted, the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus is continuously mutating, which leads to the emergence of variants with increased transmissibility, virulence, and lower response to vaccines. One important question is whether surveillance testing is still needed in order to limit SARS-CoV-2 transmission in an increasingly vaccinated population. In this talk, I will present multi-scale immuno-epidemiological mathematical models of SARS-CoV-2 transmission, and use them to determine the effects of vaccine uptake; surveillance testing with tests of different sensitivity, cost, testing frequency, and delay in test return; and testing strategies in limiting an outbreak with variants of increased infectiousness. Biography: Check https://math.vt.edu/people/faculty/ciupe-stanca.html
1:25 - 1:30 PM
Health Break
1:30 – 3:55 PM
Contributed talks (6 Talks - 20 minutes each + 4 minutes question and Speaker Change)
Session Chair: Peter Rashkov
Chapin S. Korosec, York University
Longitudinal Assessment of SARS-CoV-2 Specific T Cell Cytokine-Producing Responses for 1 Year Reveals Persistence of Multi-Cytokine Proliferative Responses, with Greater Immunity Associated with Disease Severity
Cellular-mediated immunity is critical for long-term protection against most viral infections, including coronaviruses. We studied 23 SARS-CoV-2-infected survivors over a one year post symptom onset (PSO) interval by ex vivo cytokine ELISpot assay. All subjects demonstrated SARS-CoV-2-specific IFNy, IL-2, and Granzyme B (GzmB) T cell responses at presentation, with greater frequencies in severe disease. Cytokines, mainly produced by CD4+ T cells, targeted all structural proteins (Nucleocapsid, Membrane, Spike) except Envelope, with GzmB > IL-2 > IFNy. In this talk, I will present our mathematical modelling results which predicted that: 1) cytokine responses peaked at 6 days for IFNy, 36 days for IL-2, and 7 days for GzmB, 2) severe illness was associated with reduced IFNy and GzmB, but increased IL-2 production rates, and 3) males displayed greater production of IFNy, whereas females produced more GzmB. We found ex vivo responses declined over time with persistence of IL-2 in 86% and of IFNy and GzmB in 70% of subjects at a median of 336 days PSO. The average half-life of SARS-CoV-2-specific cytokine-producing cells was modelled to be 139 days (~4.6 months). Potent T cell proliferative responses persisted throughout observation, were CD4 dominant, and were capable of producing all 3 cytokines. Our findings highlight the relative importance of SARS-CoV-2-specific GzmB-producing T cell responses in SARS-CoV-2 control, shared CD4 and CD8 immunodominant epitopes in seasonal coronaviruses or SARS-CoV-1, and indicate robust persistence of T cell memory at least one year after infection. Our findings should inform future strategies to induce T cell vaccines against SARS-CoV-2 and other coronaviruses. [bioRxiv DOI: https://doi.org/ 10.1101/2022.01.18.476864]
Gergely Röst, University of Szeged, Hungary
A hybrid PDE–ABM model for viral dynamics with application to SARS-CoV-2 and influenza
We propose a hybrid partial differential equation–agent-based (PDE–ABM) model to describe the spatio-temporal viral dynamics in a cell population. The virus concentration is considered as a continuous variable and virus movement is modelled by diffusion, while changes in the states of cells (i.e. healthy, infected, dead) are represented by a stochastic ABM. The two subsystems are intertwined: the probability of an agent getting infected in the ABM depends on the local viral concentration, and the source term of viral production in the PDE is determined by the cells that are infected. We develop a computational tool that allows us to study the hybrid system and the generated spatial patterns in detail. We systematically compare the outputs with a classical ODE system of viral dynamics, and find that the ODE model is a good approximation only if the diffusion coefficient is large. We demonstrate that the model is able to predict SARS-CoV-2 infection dynamics, and replicate the output of in vitro experiments. Applying the model to influenza as well, we can gain insight into why the outcomes of these two infections are different.
Ruth Bowness, University of Bath, UK
Modelling within-host tuberculosis infection using a hybrid multiscale individual-based model
Modelling within-host tuberculosis infection using a hybrid multiscale individual-based modelTuberculosis (TB) is an infectious disease caused by Mycobacterium tuberculosis. Despite significant recent advances, TB is the biggest infectious killer globally - someone dies from the disease every 15 seconds. I will describe a hybrid multiscale individual-based model that has been developed to study disease progression and treatment in the human lung. The model contains discrete agents which model the spatio-temporal interactions (migration, binding, killing etc.) of bacteria and immune cells. Chemokine and oxygen dynamics are also included, as well as Pharmacokinetic/Pharmacodynamic models, which are incorporated into the model via PDEs. In this work, I explore concepts of relapse and latent TB disease, and their effect on treatment outcome.
Hana Dobrovolny, Texas Christian University, USA
Using mathematical models to estimate virus-mediated cell fusion rate
Ava Amideia, and Hana M. Dobrovolnya
aDepartment of Physics & Astronomy, Texas Christian University, Fort Worth, TX
Many viruses have the ability to cause neighboring cells to fuse into multi-nucleated cells called syncytia. Much is still unknown about how syncytia affect the course of viral infection, including the time scale over which the syncytia form. Using data from a recent study of virus-mediated cell fusion in SARS-CoV-2, we use mathematical modeling to estimate the fusion rate of SARS-CoV-2 in the presence and absence of furin. We find that the presence of furin increases the fusion rate.
Lale Asik, University of the Incarnate Word, USA
Nutrient-mediated pathogen infectivity and host immunity in primary producers
Pathogens rely on their host for reproduction and changes in primary producer nutrition can thus alter their disease dynamics. At the same time, hosts rely on the availability of nutrients for their growth, as well as for their defense against pathogens. Enhanced nutrient loads may thus promote faster pathogen transmission through increased pathogen reproduction, as well as through a higher host biomass that will stimulate density-dependent infections. In contrast, nutrients may reduce pathogen transmission by stimulating the host immune response. Here, we explored the implications of nutrient-mediated pathogen infectivity and host immunity on infection outcomes using a newly developed disease model. In traditional disease models, transmission is rarely dependent on nutrients. Our nutrient-mediated transmission model explicitly integrates the contrasting dependences of pathogen infectivity and host immunity on nitrogen (N). Our findings reveal dynamic shifts in host biomass build-up, pathogen prevalence, and force of infection, along N supply gradients with N-dependent host infectivity and immunity compared to a fixed transmission model. We show contrasting responses in pathogen performance with increasing N supply between N-dependent infectivity and immunity, revealing an optimum for pathogen transmission at intermediate N supply. This is caused by N limitation of the pathogen at low N supply, and by pathogen suppression resulting from enhanced host immunity at high N supply. By integrating both nutrient-mediated pathogen infectivity and host immunity, we provide a theoretical framework that is a first step in reconciling the contrasting role nutrients can have on host pathogen interactions.
Claus Kadelka, Iowa State University
Evaluating the United States COVID-19 vaccine prioritization strategy, and how the optimal strategy might change for future roll-outs of variant-specific vaccines
Anticipating an initial shortage of vaccines for COVID-19, the Centers for Disease Control (CDC) in the United States developed, in December 2020, priority vaccine allocations for specific demographic groups in the population. We recently evaluated the performance of the CDC vaccine allocation strategy with respect to multiple potentially competing vaccination goals (minimizing mortality, cases, infections, and years of life lost), under the same framework as the CDC allocation: four priority vaccination groups and population demographics stratified by age, comorbidities, occupation and living condition (congested or non-congested). In this talk, I will briefly describe our findings, which are based on a detailed compartmental disease model that incorporates key elements of the current pandemic including age-varying susceptibility to infection, age-varying clinical fraction, and an active case-count dependent social distancing level. I will then describe current extensions of this model, which we use to predict an optimal roll-out strategy for new, initially limited COVID-19 vaccines that can specifically target an emerging variant. We use the omicron variant as a case study. The model extensions include waning immunity, reinfections, two virus variants (delta and omicron) and variant-specific immunity levels. The developed approach can highlight differences between the optimal vaccine prioritization strategy for the first roll-out and a future second roll-out. These differences are mainly due to varying levels of immunity in the different sub-populations.
3:55 - 4:00 PM
Health Break
4:00 - 4:50 PM
Keynote Address 2 (Introductions: Miranda Teboh-Ewungkem)
Dr. Jane Heffernan, PhD, Faculty of Science - Department of Mathematics & Statistics, York Research Chair (Tier II), Multi-Scale Methods for Evidence-based Health Policy; Director of the Centre for Disease Modelling
Modelling Immunity
Abstract: Immunity is generated from infection and vaccination. While immunity is gained at the individual level, we can also think of immunity as a population-level quantity as well, specifically when discussing seroprevalance and herd immunity. In this talk we will discuss the multi-scale considerations of immunity, and of immunity modelling. Influenza and COVID-19 will be of particular focus. Biography: Check https://jmheffer.mathstats.yorku.ca/
4:50 - 5:00 PM
Health Break
5:00 - 6:00 PM
Panel Session: Honoring Prof. Fred Brauer: This session honors Prof. Fred Brauer who passed away on October 17, 2021 in Vancouver, BC, Canada. Prof. Brauer was a kind man, a good mentor who made impactful contribution to the field of Mathematical Biology, especially in Mathematical Epidemiology. He will be truly missed. This session brings together some of the colleagues and past students who worked with him. Also see In Memoriam: Fred Brauer: https://math.wisc.edu/2021/10/18/in-memoriam-fred-brauer/
Panelists:
- Prof. Carlos Castillo-Chavez (Retired)
- Prof. Daniel Coombs (Professor and Head, Mathematics Department, Institute of Applied Mathematics, University of British Columbia)
- Prof. Zhilan Feng (NSF-DMS Program Director and also Department of Mathematics, Purdue University)
- Dr. Jummy Funke David (Postdoctoral Research Visitor, Department of Mathematics and Statistics and the Centre for Disease Modelling (CDM), York University, Canada)
- Prof. Aziz Yakubu (Department of Mathematics, Howard University)
Moderator: Jane Heffernan
Monday, February 28, 2022
NOTE: All Times are in Eastern Standard Time (NEW York Time)
9:00 – 11:25 AM
Contributed talks (9 Talks – 15 minutes + 1 minutes of questions/ speaker change)
Session Chair: Joshua Caleb MacDonald and Girma Mesfin Zelleke
Baylor Fain, Texas Christian University, USA
Viral master-equation: Connecting previous and current computational virology research methods
Baylor Fain and Hana Dobrovolny
The most common mathematical model in computational virology is a system of ordinary differential equations. This type of model is used for both in-host models and population level models. Due to an ordinary differential equation model treating the system as a well-mixed system, spatial heterogeneity is not captured in these models. For this reason, agent-based models have grown in popularity because they account for spatial effects. Previous work has shown that ordinary differential equation models and agent-based models can capture the dynamics of the same system, but the parameters from the two separate models are not comparable. This work aims to show how the two sets of parameters can be linked to each other by modeling a system first with a master-equation and then deriving the ordinary differential equation model and agent-based model from the master-equation.
Yuyi Xue, University of Ottawa & Xi'an Jiaotong University, Canada and China
Coupling the within-host process and between-host transmission of COVID-19 suggests closing schools is critical
Most models of COVID-19 are implemented at a single micro or macro scale, ignoring the interplay between immune response, viral dynamics, individual infectiousness and epi demiological contact networks. Here we develop a data-driven model linking the within-host viral dynamics to the between-host transmission dynamics on a multi-layer contact network to investigate the potential factors driving transmission dynamics and to inform how school closures and antiviral treatment influence the epidemic. Using multi-source data, we initially determine the viral dynamics and estimate the relationship between viral load and infectious ness. Then, we embed the viral dynamics model into a four-layer contact network and formu late an agent-based model to simulate between-host transmission. The results illustrate that the heterogeneity of immune response between children and adults and between vaccinated and unvaccinated infections can reproduce different transmission patterns. We find that school closures play a small role in suppressing viral transmission for the first wave. However, dur ing subsequent epidemic waves, school closures can have a significant effect on the pandemic. If vaccine effectiveness against infection is low, expanding vaccination coverage to younger ages (14–18 years old) would be more effective than implementing vaccine boosters. Multi scale modelling thus reveals the critical role played by younger individuals in maintaining the epidemic.
William Kwabena Osei, University of Energy and natural resource, Ghana
Mathematical dynamics of covid-19 with vaccination.
Covid-19 remains the concern of the globe as governments struggle to defeat the pandemic. Understanding the dynamics of the epidemic is as important as detecting and treatment of infected individuals. Mathematical models play a crucial role in exploring the dynamics of the outbreak by deducing strategies paramount for curtailing the com partmental model of COVID-19, with the purpose of providing insight into the dynamics of the disease by underlying tailored strategies designed to minimize the pandemic. We first studied the constant control model’s dynamic behavior by calculating the reproduction number and further examining the two nonnegative equilibria’ existence and stability. The model utilizes the Lyapunov function to investigate the global stability of the disease. To help contain the spread of the dis ease, we formulated a new SVEQIAHR compartmental optimal control model with time-dependent controls: personal protection, quarantine of the exposed, hospital ization of the quarantine, symptomatic and asymptomatic infectious individuals, and solved it by utilizing Pontryagin’s maximum principle after studying the dy namical behavior of the constant control model. The model was solved numerically by considering different pairing of the simulation controls, and the results were examined for their effectiveness.disease. The research extensively studies the SEQIAHR
Bevelynn Williams, University of Leeds, UK
Multi-scale modelling of bacterial infections
Bevelynn Williams ∗1, Martın Lopez-Garcıa 1, Joseph J. Gillard 2, Thomas R. Laws 2, Grant Lythe 1, Jonathan Carruthers 3, Thomas Finnie 3, Carmen Molina-Parıs 1,4
1University of Leeds, Leeds, United Kingdom
2Defence Science and Technology Laboratory, Salisbury, United Kingdom
3UK Health Security Agency, Salisbury, United Kingdom
4 Los Alamos National Laboratory, Los Alamos, NM, USA
mm15bw@leeds.ac.uk (*presenter), m.lopezgarcia@leeds.ac.uk, jgillard@dstl.gov.uk, trlaws@dstl.gov.uk, g.d.lythe@leeds.ac.uk, jonathan.carruthers@phe.gov.uk, thomas.finnie@phe.gov.uk, molina-paris@lanl.gov
In epidemic models, the rate at which susceptible individuals become infected incorporates a variety of factors. For example, the infection rate depends on how much contact individuals have with the pathogen. This could be from inhalation of an airborne pathogen, or through close contact with infected individuals, for example. If an individual becomes exposed to the pathogen, it is possible that their immune system will be capable of clearing the pathogen, without resulting in a detectable infection. However, in some cases the infection cannot be contained, and an infection will become established. Hence, an important factor to be incorporated into the infection rate is the likelihood that infection becomes established, given a known initial dose of the pathogen. In this talk, we will focus on a multi-scale model approach, applied to infections with the bacteria Bacillus anthracis and Francisella tularensis. This approach involves constructing individual models for the intracellular, within-host, and population-level infection dynamics, to define key quantities characterising infection at each level, which can be used to link dynamics across scales. At the intracellular scale, we consider a stochastic, Markov chain model for the intracellular infection dynamics of B. anthracis in a single phagocyte, incorporating spore germination and maturation, bacterial proliferation and death, and the possible release of bacteria due to cell rupture. This model can be used to estimate the rupture size distribution for infected phagocytes, as well as the mean time until phagocyte rupture and bacterial release. These are key quantities that can be incorporated into a within-host model of infection. We will discuss how this stochastic modelling approach can allow us to quantify and predict individual infection risk
Girma Mesfin Zelleke, University of Buea, Cameroon
A Mathematical Model of Immune Responses for Bacterial Infection: A Mathematical and Numerical Study of Active Complement System Response
Girma Mesfin Zelleke⋕∳, Miranda I. Teboh-Ewungkem∗, Gideon Akumah Ngwa
⋕ University of Buea, Cameroon
∗ Lehigh University, U.S.A
∳ African Institute for Mathematical Sciences (AIMS-Cameroon)
The cells of the immune system are divided into two main subsystems called innate and adaptive systems. These systems play significant roles in human health by protecting from foreign invaders, such as bacteria which contains inflammatory or allergic substances that attack the ability to maintain a relatively stable internal state even if there is an injury on the physical body. However, these defense mechanisms are perilous if the activation is abnormal, inefficient, and overstimulated, or if there are deficiencies in a surface-bound with receptors of the invaders. It is therefore vital that the immune system binds with an invading bacterium successfully allowing the cascade of events that will enable a proper stimulation of the defensive mechanism by the system. The innate immune system responds to bacterial infections first by activating the fastest defense mechanism called the complement system (CS). This system is controlled by more than 35 different proteins that work as a team to damage the invader and to alert other immune systems. Undoubtedly, the human immune system is enormously complex. The science of mathematical modeling enhances the study of complex system and serve as a bridge to formalize available biological knowledge into a quantitative description of the dynamical system and reproducible qualitative conclusions. So here, we propose a mathematical model which describes and captures the dynamics of the human immune system against bacterial infection. In particular, we start our interest by inspecting how active CS bridges innate and adaptive immunity. We further investigate the mathematical and numerical analysis of the model for the complement system which generates and explains conditions for further study on the dynamics of the human immune system.
Leah LeJeune (Kaisler), University of Louisiana at Lafayette, USA
Effect of cross-immunity in a multi-strain cholera model
Observed in recent cholera outbreaks is the presence of two serotypes, strains of the cholera bacteria that mainly differ in their induced host immunity. Each serotype induces both self immunity and a degree of cross-immunity to the other strain for some duration. We explore various ways of incorporating host immunity into a multi-strain cholera model, characterizing the dynamics and serotype coexistence.
Bime Markdonal Ghakanyuy, University of Buea, Cameroon
Investigating the Impact of Multiple Feeding Attempts on Mosquito Dynamics via Mathematical Models
Abstract: A deterministic differential equation model for the dynamics of terrestrial forms of mosquito populations is studied. The model assesses the impact of multiple probing attempts by mosquitoes that quest for blood within human populations by including a waiting class for mosquitoes that failed a blood feeding attempt. The equations are derived based on the idea that the reproductive cycle of the mosquito can be viewed as a set of alternating egg laying and blood feeding outcomes realized on a directed path called the gonotrophic cycle pathway. There exists a threshold parameter, the basic offspring number for mosquitoes, whose nature is affected by the way we interpret the transitions involving the different classes on the gonotrophic cycle path. The trivial steady state for the system, which always exists, can be globally asymptomatically stable whenever the threshold parameter is less than unity. The non-trivial steady state, when it exists, is stable for a range of values of the threshold parameter but can also be driven to instability via a Hopf bifurcation. The model's output reveals that the waiting class mosquitoes do contribute positively in sustaining mosquito populations as well as increase their interactions with humans via increased frequency and initial amplitude of oscillations. A nonlinear analysis, based on the center manifold theory, is used to derive expressions for the amplitude and phase of the oscillating solutions. We conclude that to understand human-mosquito interactions, it is informative to consider multiple probing attempts; known to occur when mosquitoes quest for blood meals within human populations.
Audrey McCombs, Iowa State University, USA
Structure Matters: Network topology and disease dynamics
Presenter: Audrey McCombs Co-author: Claus Kadelka
Disease dynamics depend not only on the biological properties of the pathogen, but also on the cultural climate in which the disease occurs. Human-to-human transmission events take place in the context of social interaction networks, and the structure of those networks can strongly influence how a disease spreads through a population. In this talk, I'll discuss specific network structures that have been found in empirical social networks, and how those structures explain certain epidemiological phenomena such as recent measles outbreaks. I'll describe a new technique for building networks that include key structures and investigate what these network models can tell us about the current pandemic.
Joshua Caleb Macdonald, University of Louisiana at Lafayette, USA
Consilience in FMDV ecology: Transmission dynamics in host populations reflect viral replication and immune response rates within hosts.
J.C. Macdonld, H. Gulbudak, B. Beechler, E. Gorsich, S. Gubbins, E. Perez, A. Jolles
Infectious disease dynamics operate across biological scales: pathogens replicate within hosts, but transmit among hosts and populations. Functional changes in the pathogen-host interaction thus generate cascading effects from molecular to landscape scales. Linking pathogen dynamics across biological scales is a central challenge in disease ecology. We investigated within-host dynamics and among-host transmission of three strains of foot-and-mouth disease viruses (FMDVs) in their wildlife host, African buffalo. We combined data on viral dynamics and host immune responses with mathematical models to ask (i) How do viral and immune dynamics vary among FMDV strains?; (ii) Which viral / immune parameters determine viral fitness within hosts?; and (iii) How do within-host dynamics relate to virus transmission among hosts? Our data reveal contrasting within-host dynamics among viral strains. SAT1 had the highest growth rate, followed by SAT2, and much slower growth in SAT3. However, SAT2 elicited more rapid and effective immune responses than SAT1 and SAT3. Within-host viral fitness was overwhelmingly determined by variation among hosts in immune response activation rates against FMDVs, but not by variation among viral strains in growth rate. By contrast, our analyses investigating across-scale linkages indicate that viral growth rate in the host correlates with transmission rates among buffalo; and that adaptive immune activation rate determines the infectious period. Together, these parameters define the basic reproductive number (R0) of the virus, suggesting that viral invasion potential may be predictable from within-host dynamics. Future work should test the generality of these findings by including additional FMDV strains, and create a multi-scale model to link within-host and between-host dynamics explicitly.
11:25 - 11:30 PM
Health Break
11:30 - 12:20 PM
Keynote Address 3 (Introductions: Stanca Ciupe)
Dr. Joshua T. Schiffer, M.D., M.Sc., Professor, Vaccine and Infectious Disease Division, Fred Hutch; Professor, Clinical Research Division, Fred Hutch; Associate Professor, Department of Medicine, University of Washington; Attending Physician, Infectious Disease Consulting Service, Seattle Cancer Care Alliance
A herpes virologist’s guide to SARS-CoV-2
Abstract: Human herpesviruses are chronic persistent infections which have dramatically different patterns of transmission, reactivation and disease manifestations. Over the last decade, our group has used viral dynamic modeling to capture the interactions of several of these viruses (HSV-2, CMV, EBV and HHV6) with the host immune system. We also developed methods to simulate therapies and various prevention modalities. These studies allowed our group to move rapidly into COVID-19 research to study the timing and intensity of immune responses against SARS-CoV-2, the optimal timing of therapy, the role of superspreading, the impact of masking and vaccination on transmission dynamics, the dynamics of endogenous antibody response against the virus and the local epidemiology in King County, Washington.
Biography: Check here https://www.fredhutch.org/en/faculty-lab-directory/schiffer-joshua.html
12:20 - 12:45 PM
Lunch Break
12:45 – 1:33 PM
Contributed talks (2 talks – 20 minutes + 4 minutes question/speaker change)
Session Chair: Julie Spencer
Andrea Pugliese, University of Trento, Italy
Immune memory build-up in models of repeated infections; how does this affect epidemic dynamics?
It is well known that memory cells can help to build a quick immune response in case of a new infection with the same (or similar) pathogen. This is indeed the principle at the basis of vaccination. It is also known that for certain pathogens a single vaccine dose can be insufficient to achieve a complete control of an infection, and that a second dose may be necessary. On the other hand, in several models of virus-immune interactions, the lower is the immune level before an infection, the higher it will be afterwards. This property is an important feature of the immuno-epidemiological models developed recently by Diekmann and co workers. Recently, Zarnitsyna et al. have proposed a realistic model for immune response to infection by influenza virus that results in a progressive build-up of immune memory. In the talk, I will discuss several simplifications of the model in order to assess which components of the model are essential for its qualitative behaviour. Furthermore I will show how these features can be incorporated in a consistent multi-scale epidemic models, where the susceptible population is stratified through the number of times it has been infected. Strain coexistence is then common, and potential evolutionary consequences are explored.
Narmada Sambaturu, Los Alamos National Laboratory, USA
Role of genetic heterogeneity in determining the epidemiological severity of H1N1 influenza
Narmada Sambaturu, Sumanta Mukherjee, Martín López-García, Carmen Molina-París, Gautam I. Menon, Nagasuma Chandra
Genetic differences contribute to variations in the immune response mounted by different individuals to a pathogen. Such differential response can influence the spread of infectious disease. Accounting for such variations is a major challenge for the epidemiology of infectious diseases. We propose a novel method to study the impact of population-level genetic heterogeneity on the epidemic spread of different strains of H1N1 influenza. Our results show that larger genetic diversity at the level of CD8 T-cell epitope binding, leading to the presence of susceptibility sub-populations with a broad distribution of susceptibilities, protects against the spread of influenza in a population.
1:40 - 2:50 PM - “The Debate” Cluster Topics: (1) How much do we really know about immunology? (2) Does incorporating multiple scales really bring enhanced understanding of a system? (3) What is the value of data-free and/or data-driven models?
Panelists:
- Prof. Fred Adler (University of Utah)
- Prof. Lauren Childs (Virginia Tech)
- Prof. Veronika I. Zarnitsyna (Emory University)
Chaired by Prof. Adler
2:50 - 2:55 PM
Health /Coffee Break
2:55 – 4:55 PM
Contributed talks (5 talks – 20 minutes + 4 minutes question/speaker change)
Session Chair: Julie Spencer
Tahmineh Azizi, Florida State University Department of Mathematics, USA
How does vaccine control the spread of infectious diseases?
The relationship between epidemiology, mathematical modeling and computational tools lets us to build and test theories on the development and fighting with a disease. In the current work, we study two infectious disease models and we use nonlinear optimization and optimal control theory which helps to find strategies towards transmission control and to forecast the international spread of the infectious diseases. This study is motivated by the study of epidemiological models applied to infectious diseases in an optimal control perspective. We use the numerical methods to display the solutions of the optimal control problems to find the effect of vaccination on these models. Finally, global sensitivity analysis LHS Monte Carlo method using Partial Rank Correlation Coefficient (PRCC) has been performed to investigate the key parameters in model equations. This present work will advance the understanding about the spread of infectious diseases and lead to novel conceptual understanding for spread of them.
Glenn Ledder, University of Nebraska-Lincoln
Modeling Vaccination for a Novel Disease
Abstract: Vaccination is usually added to a disease model in the form of a single-phase transition process that moves individuals from the Susceptible class to the Removed class. While this is a reasonable choice for some settings, it is problematic for others. In the case of COVID-19, there are a number of features of vaccination that are not well represented by the simplest model: (1) A significant fraction of the population consists of vaccine refusers, (2) initial supplies of vaccine are limited, (3) vaccination is more effective at limiting the severity of an infection than at preventing infection, (4) vaccination is initially target to the most vulnerable, and (5) vaccination requires two doses rather than one. While these features can all be built into a complicated model, it is not so clear how to build them into a simpler model with minimal demographic stratification. In this talk, we present a model that can be added to a simple epidemic model and addresses the first four items on the above list of features (the fifth being relatively less important when the focus is on general trends and not temporal details).
Imelda Trejo, Los Alamos National Laboratory, USA
A modified Susceptible-Infected-Recovered model for observed under-reported incidence data
Abstract: Fitting Susceptible-Infected-Recovered (SIR) models to incidence data is problematic when a fraction of the infected individuals are not reported. Assuming an underlying SIR model with general but known distribution for the time to recovery, we introduce a system of differential-integral equa tions to estimate the fraction of under-reported cases during an epidemic outbreak. Using these equations, we develop a stochastic model for the observed cases given the past time series and apply Bayesian methods to estimate the model parameters. We demonstrate our model by inferring the transmission rate and fraction of asymptomatic individuals for the current Coronavirus 2019 pandemic in eight American Countries: the United States of America, Brazil, Mexico, Argentina, Chile, Colombia, Peru, and Panama, from January 2020 to May 2021. Our analysis reveals that the percentage of under-reporting varies both between countries and over time. For example, the under-reporting of COVID-19 in the United States of America varies be tween 40% to 70%, whereas in Brazil, the under-count varies between 60% to 80%.
Jacques Bélair, Universite de Montreal, Canada
Co-Authors: FRANÇOIS BÉRUBÉ
Transmission Dynamics of COVID-19 in Elderly Residences
We consider a multiple group epidemiological model in a heterogeneous population to describe COVID-19 outbreaks in an elderly residential population. Age-based heterogeneity reflects higher transmission with enhanced interactions, and higher fatality rates in the elderly. Mathematically, we analyse a SEIR model in the form of a system of integro-differential equations with general distribution function for the infectious period. Lyapunov functions and graph-theoretical methods are employed to establish the rôle played by the basic reproduction ration R_0 : global asymptotic stability of the disease-free equilibrium and no sustained outbreak when R_0 < 1, as opposed to persistent outbreak and globally asymptotic endemic equilibrium when R_0 > 1 . Numerical simulations are presented to illustrate public health control stategies.
Michael Pablo, Gladstone Institutes / UCSF, USA
Modeling and validation of SARS-CoV-2 transmission reduction by a therapeutic interfering particle
The high transmissibility of SARS-CoV-2 continues to drive the pandemic. Vaccine deployment has shown tremendous success in limiting the severity of COVID-19 infections, but effective antiviral interventions that can curb transmission are still needed. To this end, we recently identified a therapeutic interfering particle (TIP) for SARS-CoV-2. TIPs—like classical defective interfering particles (DIPs) but engineered to have an R0>1—are non-pathogenic virus-like particles that conditionally replicate in the presence of a cognate virus, "hijacking" viral replication and packaging machinery. As a result, TIPs reduce the number of viruses produced from infected cells, and can themselves transmit to new cells. Using viral dynamics models calibrated to human clinical samples and to in vitro TIP measurements, we predicted that TIPs could substantially reduce lower respiratory tract viral loads and thus limit pathogenesis in humans, and these findings were validated by in vivo TIP studies in Syrian golden hamsters (Chaturvedi et al. Cell 2021). Then, we integrated our within-host viral dynamics model with a transmission model calibrated to contact tracing data. We predicted that TIP- mediated viral load reductions in the upper respiratory tract could substantially reduce SARS- CoV-2 transmission. Further, we predicted that limited transmission of the TIP between individuals was possible. We have now performed in vivo transmission studies with Syrian golden hamsters to test these predictions. By calibrating viral dynamics models to longitudinal hamster data, we show that TIP treatment of infected hamsters significantly reduces viral shedding for both primary infections and their secondary contacts. Our results highlight the promise of TIPs in limiting both the pathogenesis and transmission of SARS-CoV-2.
4:55 - 5:00 PM
Health Break
5:00 – 5:50 PM
Keynote Address 4 (Introductions: Lauren Childs)
Dr. Olivia Prosper, PhD, Assistant Professor of Mathematics, University of Tennessee, Tennessee
Multi-scale modeling of malaria parasite diversity
Abstract: Malaria, a parasitic disease spread by mosquitoes, imposes an enormous health and economic burden across the globe. The Ross-Macdonald mathematical framework for the transmission dynamics of malaria, developed in the early 20th century, has informed control policies for this disease and provided the basis for numerous population-level models for vector-borne disease of varying complexity. In the world of infectious disease modeling, there has been an increased interest in linking within-host pathogen dynamics to between-host transmission. I will introduce a multi-scale model of malaria that tracks parasite life cycle dynamics and parasite sequences within each mosquito and each human, as well as the transmission of these genetically diverse parasites between these two populations. The degree of parasite diversity has important implications for the transmissibility of a malaria infection and the severity of the disease for the infected human. We investigate how this diversity changes over time, and how it differs based on differences in environmental and epidemiological characteristics of the system. Biography: Check here https://math.utk.edu/people/Olivia-Prosper/
5:50 - 6:00 PM
Closing Remarks
6:00 - 6:15 PM
Happy Hour
Organizers:
Organizers:
Dr. Miranda I. Teboh-Ewungkem (Department of Mathematics, Lehigh University): Chair: Math-Epi Subgroup
Dr. Julie Allison Spencer (Los Alamos National Lab): Co-Chair/Secretary: Math-Epi Subgroup
Dr. Stanca Mihaela Ciupe (Department of Mathematics, Virginia Tech): Chair: Math-IMMU Subgroup
Dr. Amber M. Smith (The University of Tennessee Health Science Center). SMB Board of Director.