Mathematical modelling of arbovirus diseases.
ABSTRACT Arbovirus constitutes a group of virus that is transmitted by arthropod's bites. Examples of diseases produced by this kind of virus are Dengue, Yellow Fever, and West Nile Virus, among others. These diseases are a major health problem in the world. In this work we formulate a system of differential equations to study the dynamics of an infection produced by arbovirus. For this, we consider the population of host (humans, birds, mammals, etc.), and vectors (mosquitoes, ticks, etc.) The aim of this study is to understand and predict the formation of outbreaks from a variety of initial conditions. Control measures of the mosquito population are discussed in terms of threshold conditions, which govern the existence and stability of the endemic equilibrium.
- SourceAvailable from: Jorge X. Velasco-Hernandez[show abstract] [hide abstract]
ABSTRACT: We study a system of differential equations that models the population dynamics of an SIR vector transmitted disease with two pathogen strains. This model arose from our study of the population dynamics of dengue fever. The dengue virus presents four serotypes each induces host immunity but only certain degree of cross-immunity to heterologous serotypes. Our model has been constructed to study both the epidemiological trends of the disease and conditions that permit coexistence in competing strains. Dengue is in the Americas an epidemic disease and our model reproduces this kind of dynamics. We consider two viral strains and temporary cross-immunity. Our analysis shows the existence of an unstable endemic state ('saddle' point) that produces a long transient behavior where both dengue serotypes cocirculate. Conditions for asymptotic stability of equilibria are discussed supported by numerical simulations. We argue that the existence of competitive exclusion in this system is product of the interplay between the host superinfection process and frequency-dependent (vector to host) contact rates.Journal of Mathematical Biology 06/1997; 35(5):523-44. · 2.37 Impact Factor
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ABSTRACT: In this work we formulate and analyze a mathematical model for the transmission of West Nile Virus (WNV) infection between vector (mosquito) and avian population. We find the Basic Reproductive Number R0 in terms of measurable epidemiological and demographic parameters. R0 is the threshold condition that determines the dynamics of WNV infection: if R0< or =1 the disease fades out, and for R0 >1 the disease remains endemic. Using experimental and field data we estimate R0 for several species of birds. Numerical simulations of the temporal course of the infected bird proportion show damped oscillations approaching the endemic value.Bulletin of Mathematical Biology 11/2005; 67(6):1157-72. · 2.02 Impact Factor
- Transactions of the Royal Society of Tropical Medicine and Hygiene 01/1994; 88(1):58-9. · 1.82 Impact Factor