Modeling the Effects of Passive Immunity in Birds for the Disease Dynamics of West Nile Virus

West Nile Virus (WNV) is a mosquito-borne virus that circulates among birds but also affects humans. Migrating birds carry these viruses from one place to another each year. WNV has spread rapidly across the continental United States resulting in numerous human infections and deaths. Several studies suggest that larval mosquito control measures should be taken as early as possible in a season to control the mosquito population size. Also, adult mosquito control measures are necessary to prevent the transmission of WNV from mosquitoes to birds and humans. To better understand the effective strategy for controlling affected larvae mosquito population, we have developed a mathematical model using a system of first order differential equations to investigate the transmission dynamics of WNV in a mosquito-bird-human community. We also incorporated vertical transmission in mosquitoes and passive immunity in birds to more accurately simulate the spread of the disease

A Dynamical System Model of Dengue Transmission for Rio de Janeiro, Brazil

The dengue virus is a serious concern in many parts of the world, including Brazil. As data indicates, a prominent vector for dengue is the mosquito Aedes aegypti. By using the dengue incidence records from the Brazilian SINAN database, we estimate the population of A. aegypti within the city of Rio de Janeiro. Using historical climate data for Rio de Janeiro and the computed population estimates, we extend an existing model for the population dynamics of mosquitoes to incorporate precipitation in aquatic stages of development for A. aegypti

Structured Population Models: Numerical Methods and Application to Frogs Infected with Chytridiomycosis

The main objective of this dissertation is to study numerical methods and applications of structured population models. In Chapter 1, a quasilinear hierarchically size-structured population model is presented. In this model the growth, mortality and reproduction rates are assumed to depend on a function of the population density. The solutions to this model can become singular (measure-valued) in finite time even if all the individual parameters are smooth. Therefore, in this chapter we developed a first order finite difference scheme to compute these measure-valued solutions. Convergence analysis for this method was provided. We also developed a high resolution second order scheme to compute the measure-valued solution of the model and performed a comparative study between the two schemes. In Chapter 2, a model that describes the dynamics of a frog population infected with chytridiomycosis disease is presented. Chytridiomycosis is an emerging disease caused by the fungal pathogen Batrachochydrium dendrobatidis (Bd) that poses a serious threat to frog populations worldwide. Several studies have shown that inoculation of bacterial species Janthinobacterium lividum (Jl) can mitigate the impact of the disease. However, there are many questions regarding this interaction that are unknown. Therefore, a mathematical model of a frog population infected with chytridiomycosis was developed to investigate how the inoculation of Jl could reduce the impact of Bd on frogs. The model also illustrates the important role of temperature in the diseases epidemiology. The model simulation results suggest possible control strategies for Jl to limit the impact of Bd in various scenarios. Finally, in Chapter 3, concluding remarks and discussion on our future work is provided

Weighted Analytics – What Do the Numbers Suggest?

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A Dynamical Systems Model of Dengue Transmission for Rio De Janeiro, Brazil

The Dengue virus is a serious concern in many parts of the world, including Brazil. As data indicates, a prominent vector for Dengue is the Aedes Aegypti mosquito. By using the dengue incidence records from the Brazilian SINAN database, we estimate the population of Aedes aegypti within the city of Rio de Janeiro. Using historical climate data for Rio de Janeiro and the computed population estimates, we extend an existing model for the population dynamics of mosquitos to incorporate precipitation in aquatic stages of development for the Aedes aegypti mosquito