Modeling Zika

Zika is an infectious disease transmitted by Ae. aegypti and Ae. Albopictus mosquitoes species, which are found also in the US. Zika is endemic in Puerto Rico and has exhibited local transmission in Florida and Texas. Other routes of transmission of Zika are through sexual contact or from a mother to the fetus. In general Zika infection is mild but it can lead Guillain-Barré Syndrome in adults and to severe birth defects in newborns to mothers with Zika infection. We model Zika infection within the vector and the host. We consider six population-level models of Zika, which use various combinations of disease transmission (vector and direct) and infectious classes (asymptomatic and pregnant). Using cumulative incidences and cumulative pregnant incidences from the 2016 Zika outbreak in Florida, we test the models for structural and practical identifiability. We find that the models are structurally identifiable but that direct transmission rates are not practically identifiable from these data. Further, fixing the recovery rates improves overall identifiability. Elasticity analysis of the Reproduction number suggests that the mosquito-to-human ratio, mosquito life span and biting rate have the greatest potential of reducing the reproduction number of Zika. These observations imply that control measures reducing mosquito numbers, life span or biting rate would have the highest impact

A novel multi-scale immuno-epidemiological model of visceral leishmaniasis in dogs

Leishmaniasis is a neglected and emerging disease prevalent in Mediterranean and tropical climates. As such, the study and development of new models are of increasing importance. We introduce a new immuno-epidemiological model of visceral leishmaniasis in dogs. The within-host system is based on previously  collected  and published data, showing the movement and proliferation of the parasite in the skin and the bone-marrow, as well as the IgG response. The between-host system structures the infected individuals in  time-since-infection and is of vector-host type. The within-host system has a parasite-free equilibrium and at least one endemic equilibrium, consistent with the fact that infected dogs do not recover without treatment. We compute the basic reproduction number R0 of the immuno-epidemiological model  and provide the existence and stability results of the population-level  disease-free equilibrium. Additionally, we prove existence of an unique  endemic equilibrium when R0 > 1, and evidence of backward bifurcation and existence of multiple endemic equilibria when R0 < 1

Modeling the interplay between albumin-globulin metabolism and HIV infection

Human immunodeficiency virus (HIV) infection is a major public health concern with 1.2 million people living with HIV in the United States. The role of nutrition in general, and albumin/globulin in particular in HIV progression has long been recognized. However, no mathematical models exist to describe the interplay between HIV and albumin/globulin. In this paper, we present a family of models of HIV and the two protein components albumin and globulin. We use albumin, globulin, viral load and target cell data from simian immunodeficiency virus (SIV)-infected monkeys to perform model selection on the family of models. We discover that the simplest model accurately and uniquely describes the data. The selection of the simplest model leads to the observation that albumin and globulin do not impact the infection rate of target cells by the virus and the clearance of the infected target cells by the immune system. Moreover, the recruitment of target cells and immune cells are modeled independently of globulin in the selected model. Mathematical analysis of the selected model reveals that the model has an infection-free equilibrium and a unique infected equilibrium when the immunological reproduction number is above one. The infection-free equilibrium is locally stable when the immunological reproduction number is below one, and unstable when the immunological reproduction number is greater than one. The infection equilibrium is locally stable whenever it exists. To determine the parameters of the best fitted model we perform structural and practical identifiability analysis. The structural identifiability analysis reveals that the model is identifiable when the immune cell infection rate is fixed at a value obtained from the literature. Practical identifiability reveals that only seven of the sixteen parameters are practically identifiable with the given data. Practical identifiability of parameters performed with synthetic data sampled a lot more frequently reveals that only two parameters are practically unidentifiable. We conclude that experiments that will improve the quality of the data can help improve the parameter estimates and lead to better understanding of the interplay of HIV and albumin-globulin metabolism

Maia Martcheva

No biography available View Maia Martcheva\u27s website (click to view)https://commons.erau.edu/searcde-bios/1002/thumbnail.jp

An introduction to mathematical epidemiology

The book is a comprehensive, self-contained introduction to the mathematical modeling and analysis of infectious diseases. It includes model building, fitting to data, local and global analysis techniques. Various types of deterministic dynamical models are considered: ordinary differential equation models, delay-differential equation models, difference equation models, age-structured PDE models and diffusion models. It includes various techniques for the computation of the basic reproduction number as well as approaches to the epidemiological interpretation of the reproduction number. MATLAB code is included to facilitate the data fitting and the simulation with age-structured models