A simple model of coupled individual behavior and its impact on epidemic dynamics.

Containing infectious disease outbreaks is a complex challenge that usually requires the deployment of multiple intervention strategies. While mathematical modeling of infectious diseases is a widely accepted tool to evaluate intervention strategies, most models and studies overlook the interdependence between individuals' reactions to simultaneously implemented interventions. Intervention modeling efforts typically assume that individual adherence decisions are independent of each other.

Mathematical assessment of control strategies against the spread of MERS-CoV in humans and camels in Saudi Arabia.

A new mathematical model for the transmission dynamics and control of the Middle Eastern respiratory syndrome (MERS), a respiratory virus caused by MERS-CoV (and primarily spread to humans by dromedary camels) that first emerged out of the Kingdom of Saudi Arabia (KSA) in 2012, was designed and used to study the transmission dynamics of the disease in a human-camel population within the KSA. Rigorous analysis of the model, which was fitted and cross-validated using the observed MERS-CoV data for the KSA, showed that its disease-free equilibrium was locally asymptotically stable whenever its reproduction number (denoted by $ {\mathbb R}_{0M} $) was less than unity. Using the fixed and estimated parameters of the model, the value of $ {\mathbb R}_{0M} $ for the KSA was estimated to be 0.

Mathematical Assessment of the Role of Human Behavior Changes on SARS-CoV-2 Transmission Dynamics in the United States.

The COVID-19 pandemic has not only presented a major global public health and socio-economic crisis, but has also significantly impacted human behavior towards adherence (or lack thereof) to public health intervention and mitigation measures implemented in communities worldwide. This study is based on the use of mathematical modeling approaches to assess the extent to which SARS-CoV-2 transmission dynamics is impacted by population-level changes of human behavior due to factors such as (a) the severity of transmission (such as disease-induced mortality and level of symptomatic transmission), (b) fatigue due to the implementation of mitigation interventions measures (e.g.

Mathematical assessment of the roles of age heterogeneity and vaccination on the dynamics and control of SARS-CoV-2.

The COVID-19 pandemic, caused by SARS-CoV-2, disproportionately affected certain segments of society, particularly the elderly population (which suffered the brunt of the burden of the pandemic in terms of severity of the disease, hospitalization, and death). This study presents a generalized multigroup model, with heterogeneous sub-populations, to assess the population-level impact of age heterogeneity and vaccination on the transmission dynamics and control of the SARS-CoV-2 pandemic in the United States. Rigorous analysis of the model for the homogeneous case (i.

Dynamics of a two-group model for assessing the impacts of pre-exposure prophylaxis, testing and risk behaviour change on the spread and control of HIV/AIDS in an MSM population.

Although much progress has been made in reducing the public health burden of the human immunodeficiency virus (HIV), which causes acquired immunodeficiency syndrome (AIDS), since its emergence in the 1980s (largely due to the large-scale use and availability of potent antiviral therapy, improved diagnostic and intervention and mitigation measures), HIV remains an important public health challenge globally, including in the United States. This study is based on the use of mathematical modeling approaches to assess the population-level impact of pre-exposure prophylaxis (PrEP), voluntary testing (to detect undetected HIV-infected individuals), and changes in human behavior (with respect to risk structure), on the spread and control of HIV/AIDS in an MSM (men-who-have sex-with-men) population. Specifically, a novel two-group mathematical model, which stratifies the total MSM population based on risk (low or high) of acquisition of HIV infection, is formulated.

Can insecticide resistance increase malaria transmission? A genetics-epidemiology mathematical modeling approach.

The great successes recorded in the fight against malaria over the last two decades, resulting from the wide scale implementation of insecticide-based interventions in malaria-endemic areas, has prompted a renewed global effort to eradicate malaria. The widespread emergence of insecticide resistance in the population of adult female malaria mosquitoes is considered to pose a potential challenge to such effort. In this study, we address one of the key questions in malaria ecology, namely whether or not insecticide resistance increase malaria transmission.

Mathematical assessment of the role of waning and boosting immunity against the BA.1 Omicron variant in the United States.

Three safe and effective vaccines against SARS-CoV-2 have played a major role in combating COVID-19 in the United States. However, the effectiveness of these vaccines and vaccination programs has been challenged by the emergence of new SARS-CoV-2 variants of concern. A new mathematical model is formulated to assess the impact of waning and boosting of immunity against the Omicron variant in the United States.

Unraveling the dynamics of the Omicron and Delta variants of the 2019 coronavirus in the presence of vaccination, mask usage, and antiviral treatment.

The effectiveness of control interventions against COVID-19 is threatened by the emergence of SARS-CoV-2 variants of concern. We present a mathematical model for studying the transmission dynamics of two of these variants (Delta and Omicron) in the United States, in the presence of vaccination, treatment of individuals with clinical symptoms of the disease and the use of face masks. The model is parameterized and cross-validated using observed daily case data for COVID-19 in the United States for the period from November 2021 (when Omicron first emerged) to March 2022.

Mathematics of a single-locus model for assessing the impacts of pyrethroid resistance and temperature on population abundance of malaria mosquitoes.

This study presents a genetic-ecology modeling framework for assessing the combined impacts of insecticide resistance, temperature variability, and insecticide-based interventions on the population abundance and control of malaria mosquitoes by genotype. Rigorous analyses of the model we developed reveal that the boundary equilibrium with only mosquitoes of homozygous sensitive (resistant) genotype is locally-asymptotically stable whenever a certain ecological threshold, denoted by , is less than one. Furthermore, genotype drives genotype to extinction whenever and (where ,  =  or , with ≠ ).

Vaccination and herd immunity thresholds in heterogeneous populations.

It has been suggested, without rigorous mathematical analysis, that the classical vaccine-induced herd immunity threshold (HIT) assuming a homogeneous population can be substantially higher than the minimum HIT obtained when considering population heterogeneities. We investigated this claim by developing, and rigorously analyzing, a vaccination model that incorporates various forms of heterogeneity and compared it with a model that considers a homogeneous population. By employing a two-group vaccination model in heterogeneous populations, we theoretically established conditions under which heterogeneity leads to different HIT values, depending on the relative values of the contact rates for each group, the type of mixing between the groups, the relative vaccine efficacy, and the relative population size of each group.

Dynamics of COVID-19 pandemic in India and Pakistan: A metapopulation modelling approach.

India has been the latest global epicenter for COVID-19, a novel coronavirus disease that emerged in China in late 2019. We present a base mathematical model for the transmission dynamics of COVID-19 in India and its neighbor, Pakistan. The base model was rigorously analyzed and parameterized using cumulative COVID-19 mortality data from each of the two countries.

Assessing the impact of widespread respirator use in curtailing COVID-19 transmission in the USA.

Dynamic models are used to assess the impact of three types of face masks (cloth masks, surgical/procedure masks and respirators) in controlling the COVID-19 pandemic in the USA. We showed that the pandemic would have failed to establish in the USA if a nationwide mask mandate, based on using respirators with moderately high compliance, had been implemented during the first two months of the pandemic. The other mask types would fail to prevent the pandemic from becoming established.

Will vaccine-derived protective immunity curtail COVID-19 variants in the US?

Multiple effective vaccines are currently being deployed to combat the COVID-19 pandemic, and are viewed as the major factor in marked reductions of disease burden in regions with moderate to high vaccination coverage. The effectiveness of COVID-19 vaccination programs is, however, significantly threatened by the emergence of new SARS-COV-2 variants that, in addition to being more transmissible than the wild-type (original) strain, may at least partially evade existing vaccines. A two-strain (one wild-type, one variant) and two-group (vaccinated or otherwise) mechanistic mathematical model is designed and used to assess the impact of the vaccine-induced cross-protective efficacy on the spread the COVID-19 pandemic in the United States.

Toward Achieving a Vaccine-Derived Herd Immunity Threshold for COVID-19 in the U.S.

A novel coronavirus emerged in December of 2019 (COVID-19), causing a pandemic that inflicted unprecedented public health and economic burden in all nooks and corners of the world. Although the control of COVID-19 largely focused on the use of basic public health measures (primarily based on using non-pharmaceutical interventions, such as quarantine, isolation, social-distancing, face mask usage, and community lockdowns) initially, three safe and highly-effective vaccines (by AstraZeneca Inc., Moderna Inc.

Mathematical assessment of the impact of cohort vaccination on pneumococcal carriage and serotype replacement.

Although pneumococcal vaccines are quite effective in reducing disease burden, factors such as imperfect vaccine efficacy and serotype replacement present an important challenge against realizing direct and herd protection benefits of the vaccines. In this study, a novel mathematical model is designed and used to describe the dynamics of two (SP) serotypes, in response to the introduction of a cohort vaccination program which targets one of the two serotypes. The model is fitted to a pediatric SP carriage prevalence data from Atlanta, GA.

A primer on using mathematics to understand COVID-19 dynamics: Modeling, analysis and simulations.

The novel coronavirus (COVID-19) pandemic that emerged from Wuhan city in December 2019 overwhelmed health systems and paralyzed economies around the world. It became the most important public health challenge facing mankind since the 1918 Spanish flu pandemic. Various theoretical and empirical approaches have been designed and used to gain insight into the transmission dynamics and control of the pandemic.

Mathematical modeling and analysis of COVID-19 pandemic in Nigeria.

A mathematical model is designed and used to study the transmission dynamics and control of COVID-19 in Nigeria. The model, which was rigorously analysed and parametrized using COVID-19 data published by the Nigeria Centre for Disease Control (NCDC), was used to assess the community-wide impact of various control and mitigation strategies in some jurisdictions within Nigeria (notably the states of Kano and Lagos, and the Federal Capital Territory, Abuja). Numerical simulations of the model showed that COVID-19 can be effectively controlled in Nigeria using moderate levels of social-distancing strategy in the jurisdictions and in the entire nation.

Will an imperfect vaccine curtail the COVID-19 pandemic in the U.S.?

The novel coronavirus (COVID-19) that emerged from Wuhan city of China in late December 2019 continue to pose devastating public health and economic challenges across the world. Although the community-wide implementation of basic non-pharmaceutical intervention measures, such as social distancing, quarantine of suspected COVID-19 cases, isolation of confirmed cases, use of face masks in public, contact tracing and testing, have been quite effective in curtailing and mitigating the burden of the pandemic, it is universally believed that the use of a vaccine may be necessary to effectively curtail and eliminating COVID-19 in human populations. This study is based on the use of a mathematical model for assessing the impact of a hypothetical imperfect anti-COVID-19 vaccine on the control of COVID-19 in the United States.

Could masks curtail the post-lockdown resurgence of COVID-19 in the US?

The community lockdown measures implemented in the United States from late March to late May of 2020 resulted in a significant reduction in the community transmission of the COVID-19 pandemic throughout the country. However, a number of US states are currently experiencing an alarming post-lockdown resurgence of the pandemic, triggering fears for a devastating second pandemic wave. We designed a mathematical model for addressing the key question of whether or not the universal use of face masks can halt such resurgence (and possibly avert a second wave, without having to undergo another cycle of major community lockdown) in the states of Arizona, Florida, New York and the entire US.

Dynamics of a two-sex model for the population ecology of dengue mosquitoes in the presence of Wolbachia.

The release of Wolbachia-infected mosquitoes into the population of wild mosquitoes is one of the promising biological control method for combating the population abundance of mosquitoes that cause deadly diseases, such as dengue. In this study, a new two-sex mathematical model for the population ecology of dengue mosquitoes and disease is designed and used to assess the population-level impact of the periodic release of Wolbachia-infected mosquitoes. Rigorous analysis of the model, which incorporates many of the lifecycle features of dengue disease and the cytoplasmic incompatibility property of Wolbachia bacterium in mosquitoes, reveal that the disease-free equilibrium of the model is locally-asymptotically stable whenever a certain epidemiological threshold, known as the reproduction number of the model (denoted by R), is less than unity.

Long-lasting insecticidal nets and the quest for malaria eradication: a mathematical modeling approach.

Recent dramatic declines in global malaria burden and mortality can be largely attributed to the large-scale deployment of insecticidal-based measures, namely long-lasting insecticidal nets (LLINs) and indoor residual spraying. However, the sustainability of these gains, and the feasibility of global malaria eradication by 2040, may be affected by increasing insecticide resistance among the Anopheles malaria vector. We employ a new differential-equations based mathematical model, which incorporates the full, weather-dependent mosquito lifecycle, to assess the population-level impact of the large-scale use of LLINs, under different levels of Anopheles pyrethroid insecticide resistance, on malaria transmission dynamics and control in a community.

Insecticide resistance and malaria control: A genetics-epidemiology modeling approach.

Malaria, a deadly infectious disease caused by the protozoan Plasmodium, remains a major public health menace affecting at least half the human race. Although the large-scale usage of insecticides-based control measures, notably long-lasting insecticidal nets (LLINs) and indoor residual spraying (IRS), have led to a dramatic reduction of the burden of this global scourge between the period 2000 to 2015, the fact that the malaria vector (adult female Anopheles mosquito) has become resistant to all currently-available insecticides potentially makes the current laudable global effort to eradicate malaria by 2040 more challenging. This study presents a novel mathematical model, which couples malaria epidemiology with mosquito population genetics, for assessing the impact of insecticides resistance on malaria epidemiology.