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Obtaining reasonable estimates for transmission rates from observed data is a challenge when using mathematical models to study the dynamics of “infectious” diseases, like Ebola. Most models assume the transmission rate of a contagion does not vary over time. However, these rates do vary during an epidemic due to environmental conditions, social behaviors, and public-health interventions deployed to control the disease. Therefore, obtaining time-dependent rates can aid in understanding the progression of disease through a population. We derive an analytical expression using a standard SIR-type mathematical model to compute time-dependent transmission rate estimates for an epidemic in terms of either incidence or prevalence type available data. We illustrate applicability of our method by applying data on various public health problems, including infectious diseases (Ebola, SARS, and Leishmaniasis) and social issues (obesity and alcohol drinking) to compute transmission rates over time. We show that transmission rate estimates can have a large variation over time, depending on the type of available data and other epidemiological parameters. Time-dependent estimation of transmission rates captures the dynamics of the problem and can be utilized to understand disease progression through population accurately. Alternatively, constant estimations may provide unacceptable results that could have major public health consequences.

Stochastic epidemic models, generally more realistic than deterministic counterparts, have often been seen too complex for rigorous mathematical analysis because of level of details it requires to comprehensively capture the dynamics of diseases. This problem further becomes intense when complexity of diseases increases as in the case of vector-borne diseases (VBD). The VBDs are human illnesses caused by pathogens transmitted among humans by intermediate species, which are primarily arthropods. In this study, a stochastic VBD model is developed and novel mathematical methods are described and evaluated to systematically analyze the model and understand its complex dynamics. The VBD model incorporates some relevant features of the VBD transmission process including demographical, ecological and social mechanisms, and different host and vector dynamic scales. The analysis is based on dimensional reductions and model simplifications via scaling limit theorems. The results suggest that the dynamics of the stochastic VBD depends on a threshold quantity R 0 , the initial size of infectives, and the type of scaling in terms of host population size. The quantity R 0 for deterministic counterpart of the model is interpreted as a threshold condition for infection persistence as is mentioned in the literature for many infectious disease models. Different scalings yield different approximations of the model, and in particular, if vectors have much faster dynamics, the effect of the vector dynamics on the host population averages out, which largely reduces the dimension of the model. Specific scenarios are also studied using simulations for some fixed sets of parameters to draw conclusions on dynamics.

The advent of vaccinations has heightened global optimism that the end of the SARS-CoV-2 pandemic could be in sight. However, concerns, including the impact of variations in the rates of vaccination between countries, raise questions about the use of mass vaccination for accomplishing a quick recovery from the contagion. Here, we used a SEIR-based model calibrated to data on the pandemic and vaccinations reported for the United States (US) and India to gain strategic insights into using mass vaccinations for ending COVID-19. We estimate that while up to 65% of the US population is already immune to the virus due to the recent rapid mass vaccinations carried out, only 13% of the Indian population may be immune currently owing to a slow rate of vaccination and the effect of a stricter lockdown imposed to curb the first wave of the pandemic. We project that due to the higher immune to susceptible ratio already achieved in the US, the pandemic will only decline if the present rates of vaccinations and social mitigations are continued and remain effective. By contrast, the recent loosening of social measures coupled with a slow rate of vaccination is the chief reason for the virus resurgence in India, with only immediate lockdowns coupled with ramping up of vaccinations providing the means to control the present wave. These results highlight that using mass vaccination to achieve a speedy recovery from the SARS-CoV-2 pandemic will depend crucially on the ability to carry out national vaccinations as rapidly as possible.

We study a general multi-host model of visceral leishmaniasis including both humans and animals, and where host and vector characteristics are captured via host competence along with vector biting preference. Additionally, the model accounts for spatial heterogeneity in human population and heterogeneity in biting behaviour of sandflies. We then use parameters for visceral leishmaniasis in the Indian subcontinent as an example and demonstrate that the model exhibits backward bifurcation, i.e. it has a human infection and a sandfly population threshold, characterized by a bi-stable region. These thresholds shift as a function of host competence, host population size, vector feeding preference, spatial heterogeneity, biting heterogeneity and control efforts. In particular, if control is applied through human treatment a new and lower human infection threshold is created, making elimination difficult to achieve, before eventually the human infection threshold no longer exists, making it impossible to control the disease by only reducing the infection levels below a certain threshold. A better strategy would be to reduce the human infection below a certain threshold potentially by early diagnosis, control animal population levels and keep the vector population under check. Spatial heterogeneity in human populations lowers the overall thresholds as a result of weak migration between patches.

IntroductionAs SARS-COV-2 and the disease COVID-19 is sweeping through countries after countries around the globe, it is critical to understand potential burden of a future outbreak in cities of Colombia. This pandemic has affected most of the countries in the world because the high global movement of individuals and excessive cost in interventions.ObjectiveUsing demographic data from city of Cali, disease epidemiological information from affected countries and mathematical models, we estimated the rate of initial exponential growth of new cases and the basic reproductive rate for a potential outbreak in city of Cali in Colombia.Materials and methodsWe used dynamical models with different modeling assumptions such as use of various types of interventions and/or epidemiological characteristics to compare and contrast the differences between Colombian cities and between Latin American countries.ResultsUnder the assumption of homogeneously mixing population and limited resources, we predicted expected number of infected, hospitalized, in Intensive Care Units (ICU) and deaths during this potential COVID-19 outbreak. Our results suggest that on a given day in Cali there may be up to around 73000 cases who might need hospitalization under no intervention. However, this number drastically reduces if we carry out only-isolation intervention (with 16 days of symptomatic infection; ~13,000 cases) versus both quarantining for 6 days and isolation within 16 days (~3500 cases). The peak in Cali will reach in 2-3 months.ConclusionsThe estimates from these studies provides different scenarios of outbreaks and can help Cali to be better prepared during the ongoing COVID-19 outbreak.

Prevention of crops from pest has always been a serious cause of concern throughout the world, especially in agricultural countries as it contributes majorly to the economy of these countries. Keeping in mind this issue, we have formulated a mathematical model of Eggplant fruit and shoot borer which has been controlled through biological control. The dynamical analysis of the system has been discussed which includes the boundedness and positivity of the system. Local stability analysis of the system is discussed followed by local bifurcation analysis of each steady state solutions.The global stability analysis of non-trivial is done by graph theoretic approach by constructing a Lyapunov function. The optimization of the biological control strategy has also been discussed using linear feedback control. Further, we have also proposed a Spatio-temporal model and investigated it to observe the evolution of diffusive pattern in a biological pest control model. The reason of discussing the Spatio-temporal model is to focus on how diffusion can also be a method to control the pest population. The numerical simulation has been discussed to validate our analytical results obtained. Finally, we have also obtained the global sensitivity analysis using LHS method for U , x 2 and x 3 .

We create and analyze a mathematical model to understand the impact of condom-use and sexual behavior on the prevalence and spread of Sexually Transmitted Infections (STIs). STIs remain significant public health challenges globally with a high burden of some Sexually Transmitted Diseases (STDs) in both developed and undeveloped countries. Although condom-use is known to reduce the transmission of STIs, there are a few quantitative population-based studies on the protective role of condom-use in reducing the incidence of STIs. The number of concurrent partners is correlated with their risk of being infectious by an STI such as chlamydia, gonorrhea, or syphilis. We develop a Susceptible-Infectious-Susceptible (SIS) model that stratifies the population based on the number of concurrent partners. The model captures the multi-level heterogeneous mixing through a combination of biased (preferential) and random (proportional) mixing processes between individuals with distinct risk levels, and accounts for differences in condom-use in the low- and high-risk populations. We use sensitivity analysis to assess the relative impact of high-risk people using condom as a prophylactic intervention to reduce their chance of being infectious, or infecting others. The model predicts the STI prevalence as a function of the number of partners of an individual, and quantifies how this distribution of effective partners changes as a function of condom-use. Our results show that when the mixing is random, then increasing the condom-use in the high-risk population is more effective in reducing the prevalence than when many of the partners of high-risk people have high risk. The model quantifies how the risk of being infected increases for people who have more partners, and the need for high-risk people to consistently use condoms to reduce their risk of infection. Keywords: Mathematical modeling, Sexually transmitted infection (STI), Biased (preferential) mixing, Random (proportional) mixing, Condom-use, Risk (number of partners)

In several academic activities students experience a considerable stress in their daily life. Stressors may affect the mental and physical health of college students, leading some of them to the burnout syndrome. To evaluate this syndrome in students at Arizona State University (ASU), USA, a survey was conducted using a questionnaire previously developed, with ordinal variables. A theoretical Structural Equation Modeling (SEM) was proposed and the estimated model was obtained applying the Partial Least Squares (PLS) approach. Based on the PLS-SEM path coefficients, the latent construct behavioural stress has a direct effect on distress and insecurity, and an indirect effect on both quantitative demands and academic burnout. Both mediator constructs quantitative demands and distress have a direct effect on the academic burnout in students. A multi-group analysis was also conducted to compare the path coefficients of the estimated model by gender, but the differences are not statistically significant. These results allow a better understanding of burnout syndrome in ASU college students, which can severely limit their psychosocial well-being and performance.

Stochasticity provides a way to evaluate risk in complex population dynamics. This chapter describes how basic stochastic processes and algorithms are used to build models of ecological populations which can then derive probability distributions for population persistence and extinction, explain sustained oscillations generated by stochastic resonance, and measure emergent properties of a biological system, all as functions of demographic or environmental stochastic effects.

Infection of Herpes Simplex Virus type 2 (HSV-2) is a lifelong sexually transmitted disease. According to the Center for Disease Control and Prevention (CDC), 11.9% of the United States (U.S.) population was infected with HSV-2 in 2015-2016. The HSV-2 pathogen establishes latent infections in neural cells and can reactivate causing lesions later in life, a strategy that increases pathogenicity and allows the virus to evade the immune system. HSV-2 infections are currently treated by Acyclovir only in the non-constitutional stage, marked by genital skin lesions and ulcers. However, patients in the constitutional stage expressing mild and common (with other diseases) symptoms, such as fever, itching and painful urination, remain difficult to detect and are untreated. In this study, we develop and analyze a mathematical model to study the transmission and control of HSV-2 among the U.S. population between the ages of 15-49 when there are options to treat individuals in different stages of their pathogenicity. In particular, the goals of this work are to study the effect on HSV-2 transmission dynamics and to evaluate and compare the cost-effectiveness of treating HSV-2 infections in both constitutional and non-constitutional stages (new strategy) against the current conventional treatment protocol for treating patients in the non-constitutional stage (current strategy). Our results distinguish model parameter regimes where each of the two treatment strategies can optimize the available resources and consequently gives the long-term reduced cost associated with each treatment and incidence. Moreover, we estimated that the public health cost of HSV-2 with the proposed most cost-effective treatment strategy would increase by approximately 1.63% in 4 years of implementation. However, in the same duration, early treatment via the new strategy will reduce HSV-2 incidence by 42.76% yearly and the reproduction number will decrease to 0.84 from its current estimate of 2.5. Thus, the proposed new strategy will be significantly cost-effective in controlling the transmission of HSV-2 if the strategy is properly implemented.

In 2012, more than three million students dropped out from high school. At this pace, we will have more than 30 million Americans without a high school degree by 2022 and relatively high dropout rates among Hispanic and African American students. We have developed and analysed a data-driven mathematical model that includes multiple interacting mechanisms and estimates of parameters using data from a specifically designed survey applied to a certain group of students of a high school in Chicago to understand dynamics of dropouts. Our analysis suggests students' academic achievement is directly related to the level of parental involvement more than any other factors in our study. However, if the negative peer influence (leading to lower academic grades) increases beyond a critical value, the effect of parental involvement on the dynamics of dropouts becomes negligible.

The dynamics of an alcohol drinking population are subject to environment-specific control programs. The stochastic model is developed that includes populations of light, moderate, and heavy drinkers, interacting in two contrasting risk-level drinking environments. For colleges with serious drinking problems, the times to disappearance of serious drinkers show that environment-dependent control programs have lasting efficacy when they are implemented according to the risk level of the environments and not by simply focusing on heavy drinking.

Background The transmission dynamics of Tuberculosis (TB) involve complex epidemiological and socio-economical interactions between individuals living in highly distinct regional conditions. The level of exogenous reinfection and first time infection rates within high-incidence settings may influence the impact of control programs on TB prevalence. The impact that effective population size and the distribution of individuals’ residence times in different patches have on TB transmission and control are studied using selected scenarios where risk is defined by the estimated or perceive first time infection and/or exogenous re-infection rates. Methods This study aims at enhancing the understanding of TB dynamics, within simplified, two patch, risk-defined environments, in the presence of short term mobility and variations in reinfection and infection rates via a mathematical model. The modeling framework captures the role of individuals’ ‘daily’ dynamics within and between places of residency, work or business via the average proportion of time spent in residence and as visitors to TB-risk environments (patches). As a result, the effective population size of Patch i (home of i-residents) at time t must account for visitors and residents of Patch i, at time t. Results The study identifies critical social behaviors mechanisms that can facilitate or eliminate TB infection in vulnerable populations. The results suggest that short-term mobility between heterogeneous patches contributes to significant overall increases in TB prevalence when risk is considered only in terms of direct new infection transmission, compared to the effect of exogenous reinfection. Although, the role of exogenous reinfection increases the risk that come from large movement of individuals, due to catastrophes or conflict, to TB-free areas. Conclusions The study highlights that allowing infected individuals to move from high to low TB prevalence areas (for example via the sharing of treatment and isolation facilities) may lead to a reduction in the total TB prevalence in the overall population. The higher the population size heterogeneity between distinct risk patches, the larger the benefit (low overall prevalence) under the same “traveling” patterns. Policies need to account for population specific factors (such as risks that are inherent with high levels of migration, local and regional mobility patterns, and first time infection rates) in order to be long lasting, effective and results in low number of drug resistant cases.

Aims US college drinking data and a simple population model of alcohol consumption are used to explore the impact of social and contextual parameters on the distribution of light, moderate and heavy drinkers. Light drinkers become moderate drinkers under social influence, moderate drinkers may change environments and become heavy drinkers. We estimate the drinking reproduction number, R(d) , the average number of individual transitions from light to moderate drinking that result from the introduction of a moderate drinker in a population of light drinkers. Design and Settings Ways of assessing and ranking progression of drinking risks and data-driven definitions of high- and low-risk drinking environments are introduced. Uncertainty and sensitivity analyses, via a novel statistical approach, are conducted to assess R(d) variability and to analyze the role of context on drinking dynamics. Findings Our estimates show R(d) well above the critical value of 1. R(d) estimates correlate positively with the proportion of time spent by moderate drinkers in high-risk drinking environments. R(d) is most sensitive to variations in local social mixing contact rates within low-risk environments. The parameterized model with college data suggests that high residence times of moderate drinkers in low-risk environments maintain heavy drinking. Conclusions With regard to alcohol consumption in US college students, drinking places, the connectivity (traffic) between drinking venues and the strength of socialization in local environments are important determinants in transitions between light, moderate and heavy drinking as well as in long-term prediction of the drinking dynamics. Language: en

Cancer risk behaviors, including tobacco use, alcohol binge drinking, and physical inactivity, co-occur at high rates among racially and ethnically diverse college students. The overall goal of this paper is to develop a robust framework, founded on mathematical and computational models, to enhance our understanding of the social and environmental mechanisms that determine changes in health risk behavior, including alcohol binge drinking, tobacco use, and physical activity, among students enrolled in a commuter, federally designated Minority-Serving Institution in Chicago (Northeastern Illinois University, NEIU). Our underlying conceptual premise is that mutually affecting health risk behaviors spread interpersonally through social interactions and influences but can also occur spontaneously, through non-social contextual influences and increased time spent in high-risk settings. Our work acknowledges the existence of an adaptive dynamic culture of college students and incorporates a new metric, the distribution of time spent in distinct venues of students, to study its impact on population's health behaviors patterns. Our work characterizes, for the first time, social contexts of the NEIU students' diverse population and examines the effect of residence times in environments and contextual social networks on dynamics of multiple health behaviors. Our fall 2015 survey parses out social and environmental contextual pathways that are particularly relevant for college students and includes information on close friendships, peer health behavior, student allocations of time, engagement in activities on, near and off-campus and duration. Preliminary findings regarding environments in which students spend their time show that student smokers most often frequent on-campus fine arts events. All varieties of on-campus and near campus events reveal high participation rates of physically inactive students. Binge drinkers (defined as at least one episode of drinking 5 or more drinks in a row over the last 2 weeks) favored attending intercollegiate sports events over all other activity on or near campus. Intercollegiate sport events were most often frequented by students declaring multiple unhealthy behaviors. Our findings suggest to what extent (and where) interventions aimed at altering observed patterns of socialization (e.g. through tailored residence assignments or fraternity and sorority recruiting policies) and/or distribution of the times spent in students' potential environments (e.g., through sports or religious events) hold promise in controlling unhealthy behaviors among college students, especially, students of color. Citation Format: Christina Ciecierski, Brian Hitsman, Daniel Romero, Anuj Mubayi. Social activities and events and their role in determining health behavior adoption among minority college students. [abstract]. In: Proceedings of the Ninth AACR Conference on the Science of Cancer Health Disparities in Racial/Ethnic Minorities and the Medically Underserved; 2016 Sep 25-28; Fort Lauderdale, FL. Philadelphia (PA): AACR; Cancer Epidemiol Biomarkers Prev 2017;26(2 Suppl):Abstract nr A04.

Alcohol abuse is a major problem, especially among students on and around college campuses. We use the mathematical framework of [16] and study the role of environmental factors on the long term dynamics of an alcohol drinking population. Sensitivity and uncertainty analyses are carried out on the relevant functions (for example, on the drinking reproduction number and the extinction time of moderate and heavy drinking because of interventions) to understand the impact of environmental interventions on the distributions of drinkers. The reproduction number helps determine whether or not the high-risk alcohol drinking behavior will spread and become persistent in the population, whereas extinction time of high-risk drinking measures the effectiveness of control programs. We found that the reproduction number is most sensitive to social interactions, while the time to extinction of high-risk drinkers is significantly sensitive to the intervention programs that reduce initiation, and the college drop-out rate. The results also suggest that in a population, higher rates of intervention programs in low-risk environments (more than intervention rates in high-risk environments) are needed to reduce heavy drinking in the population.

The 2012-13 influenza season had an unusually early and severe start in the US, succeeding the record mild 2011-12 influenza season, which occurred during the fourth warmest winter on record. Our analysis of climate and past US influenza epidemic seasons between 1997-98 to present indicates that warm winters tend to be followed by severe epidemics with early onset, and that these patterns are seen for both influenza A and B. We posit that fewer people are infected with influenza during warm winters, thereby leaving an unnaturally large fraction of susceptible individuals in the population going into the next season, which can lead to early and severe epidemics. In the event of continued global warming, warm winters such as that of 2011-12 are expected to occur more frequently. Our results thus suggest that expedited manufacture and distribution of influenza vaccines after mild winters has the potential to mitigate the severity of future influenza epidemics.

Third political parties are influential in shaping American politics. In this work we study the spread of a third party ideology in a voting population where we assume that party members/activists are more influential in recruiting new third party voters than non-member third party voters. The study uses an epidemiological metaphor to develop a theoretical model with nonlinear ordinary differential equations as applied to a case study, the Green Party. Considering long-term behavior, we identify three threshold parameters in our model that describe the different possible scenarios for the political party and its spread. We also apply the model to the study of the Green Party's growth using voting and registration data in six states and the District of Columbia to identify and explain trends over the past decade. Our system produces a backward bifurcation that helps identify conditions under which a sufficiently dedicated activist core can enable a third party to thrive, under conditions which would not normally allow it to arise. Our results explain the critical role activists play in sustaining grassroots movements under adverse conditions.