Exploring data sources and mathematical approaches for estimating human mobility rates and implications for understanding COVID-19 dynamics: a systematic literature review.

Human mobility, which refers to the movement of people from one location to another, is believed to be one of the key factors shaping the dynamics of the COVID-19 pandemic. There are multiple reasons that can change human mobility patterns, such as fear of an infection, control measures restricting movement, economic opportunities, political instability, etc. Human mobility rates are complex to estimate as they can occur on various time scales, depending on the context and factors driving the movement. For example, short-term movements are influenced by the daily work schedule, whereas long-term trends can be due to seasonal employment opportunities. The goal of the study is to perform literature review to: (i) identify relevant data sources that can be used to estimate human mobility rates at different time scales, (ii) understand the utilization of variety of data to measure human movement trends under different contexts of mobility changes, and (iii) unraveling the associations between human mobility rates and social determinants of health affecting COVID-19 disease dynamics. The systematic review of literature was carried out to collect relevant articles on human mobility. Our study highlights the use of three major sources of mobility data: public transit, mobile phones, and social surveys. The results also provides analysis of the data to estimate mobility metrics from the diverse data sources. All major factors which directly and indirectly influenced human mobility during the COVID-19 spread are explored. Our study recommends that (a) a significant balance between primitive and new estimated mobility parameters need to be maintained, (b) the accuracy and applicability of mobility data sources should be improved, (c) encouraging broader interdisciplinary collaboration in movement-based research is crucial for advancing the study of COVID-19 dynamics among scholars from various disciplines.

Cognition and education benefits of increased hemoglobin and blood oxygenation in children with sickle cell disease.

BACKGROUND: Among individuals with sickle cell disease (SCD), decreased hemoglobin is associated with lower oxygen saturation (SpO2) and increased risk of stroke, both of which are associated with lower intelligence quotient (IQ) scores. Thus, increasing hemoglobin and SpO2 in individuals with SCD may increase IQ and educational attainment. METHODS: A cohort simulation model was built to determine academic performance and educational attainment based on cognitive function (measured by IQ) of a pediatric SCD cohort randomly assigned to treatment and control groups. The model contained two key stages: childhood (<10 years) and adolescence (≥10 years). In stage 1, increased hemoglobin and increased SpO2 (assigned to the treatment group) were determinants of higher IQ, prevention of IQ deterioration over time. Increased hemoglobin was also a determinant of decreased stroke risk. In stage 2, improvement in adolescent IQ as a result of treatment was a determinant of academic performance. RESULTS: In a simulated cohort of 2000 children and adolescents with SCD (52.5% female, 50% treated), stroke incidence was predicted to be 44.4% lower among the treated group than the untreated group (4.5% versus 8.1%, respectively). The average IQ among the treated group was estimated to be 91.1 compared with 82.9 in the untreated group (a 9.9% difference; P<0.001). Finally, high school (≥12 years of education) completion rates were estimated to be 64.7% higher among the treated group: 76.1% of the treated group was projected to complete high school compared with 46.2% of the untreated group. CONCLUSIONS: Our model predicts that an average improvement in hemoglobin of 1.1 g/dL (11 g/L) among individuals with SCD may be associated with improved neurocognition and educational outcomes. These improvements may also generate benefits not captured by our model, including improved quality of life, employment, and income.

Identifying mitigation strategies for COVID-19 superspreading on flights using models that account for passenger movement.

BACKGROUND: 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. METHODS: 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. RESULTS: 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. CONCLUSIONS: Our results suggest the need for more stringent guidelines to reduce aviation-related superspreading events of COVID-19.

Burden of cytokines storm on prognosis of SARS-CoV-2 infection through immune response: dynamic analysis and optimal control with immunomodulatory therapy.

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.

Data-driven scenario-based model projections and management of the May 2021 COVID-19 resurgence in India.

The resurgence of the May 2021 COVID-19 wave in India not only pointed to the explosive speed with which SARS-CoV-2 can spread in vulnerable populations if unchecked, but also to the gross misreading of the status of the pandemic when decisions to reopen the economy were made in March 2021. In this combined modelling and scenario-based analysis, we isolated the population and policy-related factors underlying the May 2021 viral resurgence by projecting the growth and magnitude of the health impact and demand for hospital care that would have arisen if the spread was not impeded, and by evaluating the intervention options best able to curb the observed rapidly developing contagion. We show that only by immediately re-introducing a moderately high level of social mitigation over a medium-term period alongside a swift ramping up of vaccinations could the country be able to contain and ultimately end the pandemic safely. We also show that delaying the delivery of the 2nd dose of the Astra Zeneca vaccine, as proposed by the Government of India, would have had only slightly more deleterious impacts, supporting the government's decision to vaccinate a greater fraction of the population with at least a single dose as rapidly as possible. Our projections of the scale of the virus resurgence based on the observed May 2021 growth in cases and impacts of intervention scenarios to control the wave, along with the diverse range of variable control actions taken by state authorities, also exemplify the importance of shifting from the use of science and knowledge in an ad hoc reactive fashion to a more effective proactive strategy for assessing and managing the risk of fast-changing hazards, like a pandemic. We show that epidemic models parameterized with data can be used in combination with plausible intervention scenarios to enable such policy-making.

The Hard Lessons and Shifting Modeling Trends of COVID-19 Dynamics: Multiresolution Modeling Approach.

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.

Analytical Estimation of Data-Motivated Time-Dependent Disease Transmission Rate: An Application to Ebola and Selected Public Health Problems.

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.

The role of oxygen intake and liver enzyme on the dynamics of damaged hepatocytes: Implications to ischaemic liver injury via a mathematical model.

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 different underlying medical conditions such as 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 that is often preventable if diagnosed timely. The role of mechanisms that cause IH is often not well understood, making it difficult to diagnose or accurately quantify the patterns of related biomarkers. In most patients, currently, the only way to determine a case of IH is to rule out all other possible conditions for liver injuries. A better understanding of the liver's response to IH is necessary to aid in its diagnosis, measurement, and improve outcomes. The goal of this study is to identify mechanisms that can alter associated biomarkers for reducing the density of damaged hepatocytes, and thus reduce the chances of IH. 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 the condition of IH. 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 the 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. The results may allow physicians to estimate the extent of liver damage in an IH patient based on their enzyme levels and receive faster treatment on a real-time basis.

The role of alcohol consumption on acetaminophen induced liver injury: Implications from a mathematical model.

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.

Cost analysis of treatment strategies for the control of HSV-2 infection in the U.S.: A mathematical modeling-based case study.

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.

Cost analysis of vaccination in tick-mouse transmission of Lyme disease.

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.

Complexity and critical thresholds in the dynamics of visceral leishmaniasis.

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.

Data scarcity and ecological complexity: the cutaneous leishmaniasis dynamics in Ecuador.

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 sand fly 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 CL is unknown. In this study, an epidemic model was developed and analysed to understand the complexity of CL transmission dynamics with potential non-human 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 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 programmes for Ecuador but need to be implemented concurrently to avoid future major outbreaks.

Approximation methods for analyzing multiscale stochastic vector-borne epidemic models.

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 R0, the initial size of infectives, and the type of scaling in terms of host population size. The quantity R0 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.

A Comparative Assessment of Epidemiologically Different Cutaneous Leishmaniasis Outbreaks in Madrid, Spain and Tolima, Colombia: An Estimation of the Reproduction Number via a Mathematical Model.

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.

Detecting the contagion effect in mass killings; a constructive example of the statistical advantages of unbinned likelihood methods.

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.

A Risk-based Model for Predicting the Impact of using Condoms on the Spread of Sexually Transmitted Infections.

We create and analyze a mathematical model to estimate the impact of condom-use and sexual behavior on the prevalence and spread of Sexually Transmitted Infections (STIs). STIs remain a significant public health challenge 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 quantitated 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 a STI such as chlamydia, gonorrhea, or syphilis. We define a Susceptible-Infectious-Susceptible (SIS) model that distributes the population by the number of concurrent partners. The model captures the multi-level heterogeneous mixing through a combination of biased (preferential) and random mixing between individuals with different risks, 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 to reduce their chance of being infectious, or infecting others. The model predicts the STI prevalence as a function of the number of partners that a person has, and quantifies how this distribution 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 quantified how the risk of being infected increases for people who have more partners, and and the need for high-risk people to consistently use condoms to reduce their risk of infection.

Challenges in modeling complexity of neglected tropical diseases: a review of dynamics of visceral leishmaniasis in resource limited settings.

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.