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Immune responses have a crucial role to play against SARS-CoV-2 virus as the adaptive and innate immune systems of the human body help restoring the body to a healthy stage by annihilating this deadly viral infection. Cytokines also play a significant role in modulating a balance between innate and adaptive immune responses but excess of it can have a detrimental affect on critically ill patients. Therefore, this paper is a novel attempt to formulate a within-host mathematical model showing the impact of cytokines storm on healthy cells. The dynamics of the system is analysed which involves basic reproduction number, steady state solutions and global dynamics for disease-free point and endemic equilibrium using geometric approach. Further, an optimal control problem is discussed considering immunomodulatory therapy (targeting cytokines signaling) as control using linear feedback control method to increase the level of healthy cells, which provides vitality for our system. Through numerical simulations, analytic solutions are validated followed by the curve-fit for the cytokines using real data and an optimization algorithm for optimal fit. Finally, sensitivity analysis for the basic reproduction number and the rate of change of healthy cells using Latin Hypercube Sampling method (LHS) is performed. Our finding suggests that immunomodulatory therapy (tocilizumab) can act as a key component to control cytokines storm for critically ill patients to restore the body to a healthy state.

The epidemic disease model is often used to predict an epidemic's characteristics and help plan an effective control strategy. Motivated by recent COVID-19 outbreaks, we develop and mathematically analyze a simple stochastic model that considers random perturbations in transmission rates and shows its validity using data from the Colombian city of Bogota. The stochastic epidemic model is stratified in the Susceptible-Exposed-Infectious-Recovered, \textit{SEIR}, type compartmental model with the randomness depicting the impact of stochastic variations due to external factors such as changes in environmental conditions and human behaviors that may impact the dynamics of an infectious disease. The analysis resulted in derivation of approximate distribution of \textit{eventual extinction of infection state}, \textit{persistence of infection in the mean}, and \textit{the quasi-stationary infectious state}). Finally, we illustrate inferences and model parameters using reported COVID-19 epidemic data from the Colombian city of Bogotá. The outbreak in Bogota is divided into six distinct periods, with transmission rates high during the initiation of the epidemic and even much higher during the last period, potentially due to the rapid spread of the Omicron variant in Colombia still has a low vaccination rate. Mathematics Subject Classification: 92D30

College-aged students are one of the most vulnerable populations to high-risk alcohol drinking behaviors that could cause them consequences such as injury or sexual assault. An important factor that may influence college students’ decision on alcohol drinking behavior is socializing in certain contexts across the university environment. In the present study, we aim to identify and better understand the ecological conditions driving the dynamics of distribution of alcohol use among college-aged students. To this end, a pilot survey study is conducted to evaluate students’ movement patterns in different contexts across the Arizona State University (ASU) campus, and the results are used to develop an agent-based simulation model designed for examining the role of environmental factors on development and maintenance of alcohol drinking behavior by a representative sample of ASU students. The proposed model, which resembles an approximate reaction–diffusion model, accounts for movement of agents (i.e., diffusion) in various contexts and alcohol drinking influences within those contexts (i.e., reaction) via a Susceptible-Infected-Recovered type individual-based model. Of the four most visited contexts at ASU Tempe campus—Library, Memorial Union, Fitness Center, and Dorm—the context with the highest visiting probability, Memorial Union, is the most influential and most sensitive context (around sixteen times higher an impact of alcohol-related influences than the other contexts) in terms of spreading alcohol drinking behavior. Our findings highlight the crucial role of socialization in local environments on the dynamics of students’ alcohol use as well as on the long-term prediction of the college drinking prevalence.

Schistosomiasis is one of the major neglected tropical diseases (NTDs) with more than 240 million people currently infected, primarily ( 90%) in sub-Saharan Africa. It is treated and primarily controlled through mass drug administration (MDA) in endemic regions. Determining the extent to which an intervention to control Schistosomiasis has been suc- cessful, is essential, but its evaluation become complicated by the potential for an outbreak to evolve over time via change in behaviors of individuals in the affected community. We study the role of changes in population behaviors on the patterns of Schistosomiasis via a novel transmission dynamics model which explicitly involves two free living larval stages, the Cercariae and Miracidia , and two host populations, the snail and the human. The average number of Miracidia reduces due to the change in human behaviors (like avoid wading, swimming and other contacts to contaminated water), consequently, reduction in the average number of Miracidia affect the rate of infection transmission. Thus, the model assumes that change in population behaviors indirectly affect the rate of infection transmission. Rigorous mathematical analysis on the model was carried and it suggests threshold behavior in long term dynamics governed by reproductive number R 0 . The dynamics shows existence of at least two equilibria (disease-free and endemic state) and regions of their global stability in the parameter space. Our results also suggest that removal of snails from the water bodies is most effective control strategy for elimination of Schistosomiasis infection as compared to either increasing of human treatment rates or cleaning of free-living Cercariae from local water bodies. The indirect human behav- ioral changes do not affect the likelihood of the existence/eradication of epidemic (i.e., R 0 does not depend on parameters related to behavioral change), however, their impact are critical on the endemic prevalence. Our results provide some new understanding about elimination of Schistosomiasis and could be useful for optimal distribution of resources for control programs.

The COVID-19 pandemic has placed epidemiologists, modelers, and policy makers at the forefront of the global discussion of how to control the spread of coronavirus. The main challenges confronting modelling approaches include real-time projections of changes in the numbers of cases, hospitalizations, and fatalities, the consequences of public health policy, the understanding of how best to implement varied non-pharmaceutical interventions and potential vaccination strategies, now that vaccines are available for distribution. Here, we: (i) review carefully selected literature on COVID-19 modeling to identify challenges associated with developing appropriate models along with collecting the fine-tuned data, (ii) use the identified challenges to suggest prospective modeling frameworks through which adaptive interventions such as vaccine strategies and the uses of diagnostic tests can be evaluated, and (iii) provide a novel Multiresolution Modeling Framework which constructs a multi-objective optimization problem by considering relevant stakeholders' participatory perspective to carry out epidemic nowcasting and future prediction. Consolidating our understanding of model approaches to COVID-19 will assist policy makers in designing interventions that are not only maximally effective but also economically beneficial.

Despite commercial airlines mandating masks, there have been multiple documented events of COVID-19 superspreading on flights. Conventional models do not adequately explain superspreading patterns on flights, with infection spread wider than expected from proximity based on passenger seating. An important reason for this is that models typically do not consider the movement of passengers during the flight, boarding, or deplaning. Understanding the risks for each of these aspects could provide insight into effective mitigation measures.We modeled infection risk from seating and fine-grained movement patterns - boarding, deplaning, and inflight movement. We estimated infection model parameters from a prior superspreading event. We validated the model and the impact of interventions using available data from three flights, including cabin layout and seat locations of infected and uninfected passengers, to suggest interventions to mitigate COVID-19 superspreading events during air travel. Specifically, we studied: 1) London to Hanoi with 201 passengers, including 13 secondary infections among passengers; 2) Singapore to Hangzhou with 321 passengers, including 12 to 14 secondary infections; 3) a non-superspreading event on a private jet in Japan with 9 passengers and no secondary infections.Our results show that the inclusion of passenger movement better explains the infection spread patterns than conventional models do. We also found that FFP2/N95 mask usage would have reduced infection by 95-100%, while cloth masks would have reduced it by only 40-80%. Results indicate that leaving the middle seat vacant is effective in reducing infection, and the effectiveness increases when combined with good quality masks. However, with a good mask, the risk is quite low even without the middle seats being empty.Our results suggest the need for more stringent guidelines to reduce aviation-related superspreading events of COVID-19.

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.

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.

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.

Ischaemic Hepatitis (IH) or Hypoxic Hepatitis (HH) also known as centrilobular liver cell necrosis is an acute liver injury characterized by a rapid increase in serum aminotransferase. The liver injury typically results from another underlying medical conditions like cardiac failure, respiratory failure and septic shock in which the liver becomes damaged due to deprivation of either blood or oxygen. IH is a potentially lethal condition which is often preventable if diagnosed properly. {\em Unfortunately, mechanism that causes IH are often not well understood, making it difficult to diagnose or accurately quantify the patterns of related biomarkers}. In most cases, currently the only way to determine a case of IH (i.e., to diagnose it) is to rule out all other possible conditions for other liver injuries. A better understanding of the liver9s response to IH is necessary to aid in its diagnosis, measurement and improve outcomes. {\bf The goal of this study, is to identify mechanisms that can alter a few associated biomarkers for reducing density of damaged hepatocytes, and thus reduce chances of IH}. To this end, we develop a mathematical model capturing dynamics of hepatocytes in the liver through the rise and fall of associated liver enzymes aspartate transaminase (AST), alanine transaminase (ALT) and lactate dehydrogenase (LDH) related to condition of IH. %It studies liver cell death in response to IH caused by chronic heart failure and cardiovascular shock. The model analysis provides a novel approach to predict the level of biomarkers given variations in the systemic oxygen in the body. Using IH patient data in US, novel model parameters are described and then estimated for the first time to capture real time dynamics of hepatocytes in the presence and absence of IH condition. Different scenarios of patient conditions were also analyzed and validated using empirical information. This study and its results may allow physicians to estimate the extent of liver damage in a IH patient based on their enzyme levels and receive faster treatment on real time basis.

In this paper, we present a formulation for a multiscale model combining a social force based pedestrian movement including collision avoidance and a stochastic infection dynamics framework to evaluate the spread of multiple infectious diseases during air travel. We apply the multiscale model to evaluate pedestrian movement strategies that can reduce infection spread during air travel. The results are presented for airport lounge and airplane boarding and deplaning. Use of parallel computing to evaluate the vast parameter space created due to stochasticity and discretionary pedestrian behavior is addressed.

Coronavirus disease 2019 (COVID-19), a novel infectious disease first identified in December 2019 in the city of Wuhan of China’s Hubei province, is caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). The disease has become a pandemic in just a few months and spread globally with more than 2.89 million cases and 203,000 deaths across 185 countries, as of April 26th, 2020. Ecuador has reported one of the highest rates of COVID-19 in Latin America, with more than 10K cases and 500 deaths in a country of approximately 17 million people. The dynamics of the outbreak is being observed quite different in different provinces of Ecuador with high reported prevalence in some low population density provinces. In this study, we aim to understand variations in outbreaks between provinces and provide assistance in essential preparedness planning in order to respond effectively to ongoing COVID-19 outbreak. The study estimated the critical level of quarantine rate along with corresponding leakage in order to avoid overwhelming the local health care system. The results suggest that provinces with high population density can avoid a large disease burden provided they initiate early and stricter quarantine measures even under low isolation rate. To best of our knowledge, this study is first from the region to determine which provinces will need much preparation for current outbreak in fall and which might need more help.

Acetaminophen (APAP) overdose is one of the predominant causes of drug induced acute liver injury in the U.S and U.K. Clinical studies show that ingestion of alcohol may increase the risk of APAP induced liver injury. Chronic alcoholism may potentiate APAP hepatotoxicity and this increased risk of APAP toxicity is observed when APAP is ingested even shortly after alcohol is cleared from the body. However, clinical reports also suggest that acute alcohol consumption may have a protective effect against hepatotoxicity by inhibiting microsomal acetaminophen oxidation and thereby reducing N-acetyl-p-benzoquinone imine (NAPQI) production. The aim of this study is to model this dual role of alcohol to determine how the timing of alcohol ingestion affects APAP metabolism and resulting liver injury and identify mechanisms of APAP induced liver injury. The mathematical model is developed to capture condition of a patient of single time APAP overdose who may be an acute or chronic alcohol user. The analysis suggests that the risk of APAP-induced hepatotoxicity is increased if APAP is ingested shortly after alcohol is cleared from the body in chronic alcohol users. A protective effect of acute consumption of alcohol is also observed in patients with APAP overdose. For example, simultaneous ingestion of alcohol and APAP overdose or alcohol intake after or before few hours of APAP overdose may result in less APAP-induced hepatotoxicity when compared to a single time APAP overdose. The rate of hepatocyte damage in APAP overdose patients depends on trade-off between induction and inhibition of CYP enzyme.

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.

Airlines have introduced a back-to-front boarding process in response to the COVID-19 pandemic. It is motivated by the desire to reduce passengers' likelihood of passing close to seated passengers when they take their seats. However, our prior work on the risk of Ebola spread in airplanes suggested that the driving force for increased exposure to infection transmission risk is the clustering of passengers while waiting for others to stow their luggage and take their seats. In this work, we examine whether the new boarding processes lead to increased or decreased risk of infection spread. We also study the reasons behind the risk differences associated with different boarding processes. We accomplish this by simulating the new boarding processes using pedestrian dynamics and compare them against alternatives. Our results show that back-to-front boarding roughly doubles the infection exposure compared with random boarding. It also increases exposure by around 50% compared to a typical boarding process prior to the outbreak of COVID-19. While keeping middle seats empty yields a substantial reduction in exposure, our results show that the different boarding processes have similar relative strengths in this case as with middle seats occupied. We show that the increased exposure arises from the proximity between passengers moving in the aisle and while seated. Our results suggest that airlines either revert to their earlier boarding process or adopt the better random process., Comment: 9 pages, 5 figures

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 either does not vary over time or change in a fixed pre-determined adhoc ways. However, these rates do vary during an outbreak due to multitude of factors such as environmental conditions, social behaviors, and public-health interventions deployed to control the disease, which are in-part guided by changing size of an outbreak. We derive analytical estimates of time-dependent transmission rate for an epidemic in terms of either incidence or prevalence using a standard mathematical SIR-type epidemic model. 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 time-dependent transmission rate estimates can have a large variation, depending on the type of available data and other epidemiological parameters. Time-dependent estimation of transmission rates captures the dynamics of the problem better and can be utilized to understand disease progression more accurately.

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 .

Objective To stratify and understand the potential transmission processes of Zika virus in Colombia, in order to effectively address the efforts on surveillance and disease control. Methods We compare R0, of Zika for municipalities based on data from the regional surveillance system of Antioquia, Colombia. The basic reproduction number (R0) and its 95% confidence intervals were estimated from an SIR model with implicit vector dynamics, in terms of recovered individuals in each time unit, using an approximate solution. These parameters were estimated fitting the solution of the model to the daily cumulative frequency of each Zika case according to symptoms onset date relative to the index case reported to the local surveillance system. Results R0 was estimated for 20 municipalities with a median of 30,000 inhabitants, all located less than 2,200 m above sea level. The reported cases ranged from 17 to 347 between these municipalities within four months (January to April of 2016). The results suggest that 15 municipalities had a high transmission potential (R0>1), whereas in 5 municipalities transmission were potentially not sustaining (R01) and provide a technique to optimize surveillance and control of Zika. Health authorities should promote the collection, analysis, modeling and sharing of anonymous data onto individual cases to estimate R0. This article is protected by copyright. All rights reserved.

Objectives Neglected tropical diseases (NTD), account for a large proportion of the global disease burden, and their control faces several challenges including diminishing human and financial resources for those distressed from such diseases. Visceral leishmaniasis (VL), the second-largest parasitic killer (after malaria) and an NTD affects poor populations and causes considerable cost to the affected individuals. Mathematical models can serve as a critical and cost-effective tool for understanding VL dynamics, however, complex array of socio-economic factors affecting its dynamics need to be identified and appropriately incorporated within a dynamical modeling framework. This study reviews literature on vector-borne diseases and collects challenges and successes related to the modeling of transmission dynamics of VL. Possible ways of creating a comprehensive mathematical model is also discussed. Methods Published literature in three categories are reviewed: (i) identifying non-traditional but critical mechanisms for VL transmission in resource limited regions, (ii) mathematical models used for dynamics of Leishmaniasis and other related vector borne infectious diseases and (iii) examples of modeling that have the potential to capture identified mechanisms of VL to study its dynamics. Results This review suggests that VL elimination have not been achieved yet because existing transmission dynamics models for VL fails to capture relevant local socio-economic risk factors. This study identifies critical risk factors of VL and distribute them in six categories (atmosphere, access, availability, awareness, adherence, and accedence). The study also suggests novel quantitative models, parts of it are borrowed from other non-neglected diseases, for incorporating these factors and using them to understand VL dynamics and evaluating control programs for achieving VL elimination in a resource-limited environment. Conclusions Controlling VL is expensive for local communities in endemic countries where individuals remain in the vicious cycle of disease and poverty. Smarter public investment in control programs would not only decrease the VL disease burden but will also help to alleviate poverty. However, dynamical models are necessary to evaluate intervention strategies to formulate a cost-effective optimal policy for eradication of VL. Electronic supplementary material The online version of this article (doi:10.1186/s12982-017-0065-3) contains supplementary material, which is available to authorized users.

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)

The two hyper–endemic regions for Visceral Leishmaniasis (VL) in the world are located in India and Sudan. These two countries account for more than half of the world’s VL burden. The regional risk factors associated with VL vary drastically per region. A mathematical model of VL transmission dynamics is introduced and parametrized to quantify risk of VL infection in India and Sudan via a careful analysis of VL prevalence level and the control reproductive number,, a metric often used to characterize the degree of endemicity. Parameters, associated with VL-epidemiology for India and Sudan, are estimated using data from health departmental reports, clinical trials, field studies, and surveys in order to assess potential differences between the hyper–endemic regions of India and Sudan. The estimated value of reproduction number for India is found to be 60% higher than that of Sudan (and). It is observed that theis most sensitive to the average biting rate and vector-human transmission rates irrespective of regional differences. The treatment rate is found to be the most sensitive parameter to VL prevalence in humans for both India and Sudan. Although the unexplained higher incidence of VL in India needs to be carefully monitored during long-term empirical follow-up, the risk factors associated with vectors are identified as more critical to dynamics of VL than factors related to humans through this modeling study.Author SummaryThe Visceral Leishmaniasis (VL) is a neglected tropical disease, primarily endemic in five countries, with India and Sudan having the highest burden. The risk factors associated with VL are either unknown in some regions or vary drastically among empirical studies. In this study, we collect VL-related data from multiple sources for the two different countries, India and Sudan, and use techniques from mathematical modeling to understand factors that may be critical in the spread and control of VL. The results suggest that the risk factors associated with disease progression are important in explaining high VL prevalence in both the countries. However, the likelihood of disease outbreak in India is much higher than that in Sudan and the probability of transmission between human and sandfly populations vary significantly between the two. The results have implications towards VL elimination and may require a review of current control priorities.

Background: Underreporting of Visceral Leishmaniasis (VL) in India remains a problem to public health controls. Effective and reliable surveillance systems are critical for monitoring disease outbreaks and public health control programs. However, in India, government surveillance systems are affected by levels of scarcity in resources and therefore, uncertainty surrounds the true incidence of asymptomatic and clinical cases, affecting morbidity and mortality rates. The State of Bihar alone contributes up to the 40\% of the worldwide VL cases. The inefficiency of surveillance systems occurs because of multiple reasons including delay in seeking health care, accessing non-authentic health care clinics, and existence of significant asymptomatic self healing infectious cases. This results in a failure of the system to adequately report true transmission rates and number of symptomatic cases that have sought medical advice (thus, high underreporting of cases). Objectives and Methods: There are several methods to estimate the extent of underreporting in the surveillance system. In this research, we use a mathematical dynamic model and two different types of data sets, namely, monthly incidence for 2003-2005 and yearly incidence from 2006-2012 from the Bihar's 21 most VL affected districts out of its 38 districts. The goals of the study are to estimate critical metrics to measure level of transmission and to evaluate the estimation process between the two data sets and 21 districts. In particularly, our focus is on (i) estimating infection transmission potential, underreporting level in incidence and proportion of self-healing cases, (ii) quantifying reproduction number of the$R_0$, and (iii) comparing underreporting incidence levels and proportion of self-healing cases between the two periods 2003-2005 and 2006-2012 and between 21 districts. Results: Our research suggests that the number of asymptomatic individuals in the population who eventually self-heal may have a significant effect on the dynamics of VL spread. The estimated mean self-healing proportion (out of all infected) is found to be $\sim 0.6$ with only 7 out of 21 affected districts having self-healing proportion less than $0.5$ for both data sets. The estimated mean underreporting level is at least $64$\% for the state of Bihar. The estimates of the basic reproduction numbers obtained are similar in magnitude for most of the districts, being in the range of (0.88, 2.79) and (0.98, 1.01) for 2003-2005 and 2006-2012, respectively. Conclusions: The estimates for the two types (monthly and yearly) of temporal data suggest that monthly data are better for estimation if less number of data points are available, however, in general, using such data set results in larger variances in parameters as compared to estimates obtained through aggregated yearly data. Estimated values of transmission related metrics are lower than those obtained from earlier analyses in the literature, and the implications of this for VL control are discussed. The spatial heterogeneity in these control metrics increases the risk of epidemics and makes the control strategies more complex.

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.

Cutaneous Leishmaniasis (CL) is a neglected tropical disease transmitted by species of Phlebotominae sand flies. CL is responsible for more than 1000 reported cases per year in Ecuador. Vector collection studies in Ecuador suggest that there is a strong association between the ecological diversity of an ecosystem, the presence of potential alternative or reservoir hosts and the abundance of sandfly species. Data collected from a coastal community in Ecuador showed that Leishmania parasites may be circulating in diverse hosts, including mammalian and potentially avian species, and these hosts may serve as potential hosts for the parasite. There has been limited reporting of CL cases in Ecuador because the disease is non-fatal and its surveillance system is passive. Hence, the actual incidence of the CL is unknown. In this study, an epidemic model was developed and analysed to understand the complexity of CL transmission dynamics with potential non-humans hosts in the coastal ecosystem and to estimate critical epidemiological quantities for Ecuador. The model is fitted to the 2010 CL outbreak in the town of Valle Hermoso in the Santo Domingo de los Tsachilas province of Ecuador and parameters such as CL transmission rates in different types of hosts (primary and alternative), and levels of case reporting in the town are estimated. The results suggest that the current surveillance in this region fails to capture 38% (with 95% CI (29%, 47%)) of the actual number of cases under the assumption that alternative hosts are dead-end hosts and that the mean CL reproduction number in the town is 3.9. This means that on the average 3.9 new human CL cases were generated by a single infectious human in the town during the initial period of the 2010 outbreak. Moreover, major outbreaks of CL in Ecuador in the coastal settings are unavoidable until reporting through the surveillance system is improved and alternative hosts are managed properly. The estimated infection transmission probabilities from alternative hosts to sand flies, and sand flies to alternative hosts are 27%, and 32%, respectively. The analysis highlights that vector control and alternative host management are two effective programs for Ecuador but need to be implemented concurrently to avoid future major outbreaks.

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.

Soil-transmitted helminthiasis (STH), a neglected tropical disease (NTD) remains a major health problem all over the world including Ghana, which has STH prevalence of 25.4%. To control the disease, the government of Ghana currently concentrates on implementing mass drug administration (MDA) efforts focusing only among school-aged children. However, various studies have suggested that focusing on only a specific group for MDA may not be cost-effective. Moreover, some adults such as teachers and school-workers spend large fraction of their time with children, who shed more parasite in environment due to unhygienic behavior, and thus have a higher risk of getting infected as compared to other adults. In this study we use a mathematical model to evaluate age-structured and risk-based policies for implementing MDA while capturing transmission dynamics of STH in Ghana. A cost model was developed that included various costs related to MDA to study cost-effectiveness of current policies of MDA in Ghana against novel policies to control STH in Ghana. We carry out analysis for five different scenarios— I: no MDA (baseline), II: current MDA policy (focusing children) in Ghana, III: MDA for different age groups (adults and children groups) for unlimited budget, IV: MDA for different age groups with limitations of number of individuals treated, and, V: MDA for different groups based on their risk of getting infected (adults school workers (high-risk group), adults non-school workers and children groups). Our results suggest that it might be more cost-effective to allocate treatment through MDA to at least some proportion of adults along with children. In case of unlimited budget, the best strategy in Scenario IV would be to treat approximately 22% of adults and approximately 45% of children. The most cost-effective among the 5 scenarios is suggested through scenario V, where high-risk adults group and children are provided MDA at higher level than low-risk adults. In conclusion, age-structured and risk-based allocation of treatment and resources is crucial to reducing STH load in developing countries.

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.

Lyme disease is one of the most prevalent and fastest growing vector-borne bacterial illnesses in the United States, with over 25,000 new confirmed cases every year. Humans contract the bacterium Borrelia burgdorferi through the bite of the tick Ixodes scapularis. The tick can receive the bacterium from a variety of small mammal and bird species, but the white-footed mouse Peromyscus leucopus is the primary reservoir in the northeastern United States, especially near human settlement. The tick's life cycle and behavior depend greatly on the season, with different stages of tick biting at different times. Reducing the infection in the tick-mouse cycle may greatly lower human Lyme incidence in some areas. However, research on the effects of various mouse-targeted interventions is limited. One particularly promising method involves administering vaccine pellets to white-footed mice through special bait boxes. In this study, we develop and analyze a mathematical model consisting of a system of nonlinear difference equations to understand the complex transmission dynamics and vector demographics in both tick and mice populations. We evaluate to what extent vaccination of white-footed mice can affect Lyme incidence in I. scapularis, and under which conditions this method saves money in preventing Lyme disease. We find that, in areas with high human risk, vaccination can eliminate mouse-tick transmission of B. burgdorferi while saving money.

Background When attempting to statistically distinguish between a null and an alternative hypothesis, many researchers in the life and social sciences turn to binned statistical analysis methods, or methods that are simply based on the moments of a distribution (such as the mean, and variance). These methods have the advantage of simplicity of implementation, and simplicity of explanation. However, when null and alternative hypotheses manifest themselves in subtle differences in patterns in the data, binned analysis methods may be insensitive to these differences, and researchers may erroneously fail to reject the null hypothesis when in fact more sensitive statistical analysis methods might produce a different result when the null hypothesis is actually false. Here, with a focus on two recent conflicting studies of contagion in mass killings as instructive examples, we discuss how the use of unbinned likelihood methods makes optimal use of the information in the data; a fact that has been long known in statistical theory, but perhaps is not as widely appreciated amongst general researchers in the life and social sciences. Methods In 2015, Towers et al published a paper that quantified the long-suspected contagion effect in mass killings. However, in 2017, Lankford & Tomek subsequently published a paper, based upon the same data, that claimed to contradict the results of the earlier study. The former used unbinned likelihood methods, and the latter used binned methods, and comparison of distribution moments. Using these analyses, we also discuss how visualization of the data can aid in determination of the most appropriate statistical analysis methods to distinguish between a null and alternate hypothesis. We also discuss the importance of assessment of the robustness of analysis results to methodological assumptions made (for example, arbitrary choices of number of bins and bin widths when using binned methods); an issue that is widely overlooked in the literature, but is critical to analysis reproducibility and robustness. Conclusions When an analysis cannot distinguish between a null and alternate hypothesis, care must be taken to ensure that the analysis methodology itself maximizes the use of information in the data that can distinguish between the two hypotheses. The use of binned methods by Lankford & Tomek (2017), that examined how many mass killings fell within a 14 day window from a previous mass killing, substantially reduced the sensitivity of their analysis to contagion effects. The unbinned likelihood methods used by Towers et al (2015) did not suffer from this problem. While a binned analysis might be favorable for simplicity and clarity of presentation, unbinned likelihood methods are preferable when effects might be somewhat subtle.

Leishmaniasis is a neglected tropical disease caused by the Leishmania parasite and transmitted by the Phlebotominae subfamily of sandflies, which infects humans and other mammals. Clinical manifestations of the disease include cutaneous leishmaniasis (CL), mucocutaneous leishmaniasis (MCL) and visceral leishmaniasis (VL) with a majority (more than three-quarters) of worldwide cases being CL. There are a number of risk factors for CL, such as the presence of multiple reservoirs, the movement of individuals, inequality, and social determinants of health. However, studies related to the role of these factors in the dynamics of CL have been limited. In this work, we (i) develop and analyze a vector-borne epidemic model to study the dynamics of CL in two ecologically distinct CL-affected regions—Madrid, Spain and Tolima, Colombia; (ii) derived three different methods for the estimation of model parameters by reducing the dimension of the systems; (iii) estimated reproduction numbers for the 2010 outbreak in Madrid and the 2016 outbreak in Tolima; and (iv) compared the transmission potential of the two economically-different regions and provided different epidemiological metrics that can be derived (and used for evaluating an outbreak), once R0 is known and additional data are available. On average, Spain has reported only a few hundred CL cases annually, but in the course of the outbreak during 2009–2012, a much higher number of cases than expected were reported and that too in the single city of Madrid. Cases in humans were accompanied by sharp increase in infections among domestic dogs, the natural reservoir of CL. On the other hand, CL has reemerged in Colombia primarily during the last decade, because of the frequent movement of military personnel to domestic regions from forested areas, where they have increased exposure to vectors. In 2016, Tolima saw an unexpectedly high number of cases leading to two successive outbreaks. On comparing, we estimated reproduction number of the Madrid outbreak to be 3.1 (with range of 2.8–3.9), which was much higher than reproduction number estimates of the Tolima first outbreak 1.2 (with range of 1.1–1.3), and the estimate for the second outbreak in Tolima of 1.019 (with range of 1.018–1.021). This suggests that the epidemic outbreak in Madrid was much more severe than the Tolima outbreak, even though Madrid was economically better-off compared to Tolima. It indicates a potential relationship between urban development and increasing health disparities.

Visceral leishmaniasis (VL) is the most deadly form of the leishmaniasis family of diseases, which affects numerous developing countries. The Indian state of Bihar has the highest prevalence and mortality rate of VL in the world. Insecticide spraying is believed to be an effective vector control program for controlling the spread of VL in Bihar; however, it is expensive and less effective if not implemented systematically. This study develops and analyzes a novel optimization model for VL control in Bihar that identifies an optimal (best possible) allocation of chosen insecticide (dichlorodiphenyltrichloroethane [DDT] or deltamethrin) based on the sizes of human and cattle populations in the region. The model maximizes the insecticide-induced sandfly death rate in human and cattle dwellings while staying within the current state budget for VL vector control efforts. The model results suggest that deltamethrin might not be a good replacement for DDT because the insecticide-induced sandfly deaths are 3.72 times more in case of DDT even after 90 days post spray. Different insecticide allocation strategies between the two types of sites (houses and cattle sheds) are suggested based on the state VL-control budget and have a direct implication on VL elimination efforts in a resource-limited region.