Stochastic dynamics of dengue epidemics

We use a stochastic Markovian dynamics approach to describe the spreading of vector-transmitted diseases, like dengue, and the threshold of the disease. The coexistence space is composed by two structures representing the human and mosquito populations. The human population follows a susceptible-inf...

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Bibliographic Details
Published inarXiv.org
Main Authors Souza, David R, Tomé, Tânia, Suani T R Pinho, Barreto, Florisneide R, de Oliveira, Mário J
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 28.12.2012
Subjects
Computer simulation
Disease
Dynamics
Epidemics
Markov processes
Mosquitoes
Spreading
Viral diseases
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Summary:We use a stochastic Markovian dynamics approach to describe the spreading of vector-transmitted diseases, like dengue, and the threshold of the disease. The coexistence space is composed by two structures representing the human and mosquito populations. The human population follows a susceptible-infected-recovered (SIR) type dynamics and the mosquito population follows a susceptible-infected-susceptible (SIS) type dynamics. The human infection is caused by infected mosquitoes and vice-versa so that the SIS and SIR dynamics are interconnected. We develop a truncation scheme to solve the evolution equations from which we get the threshold of the disease and the reproductive ratio. The threshold of the disease is also obtained by performing numerical simulations. We found that for certain values of the infection rates the spreading of the disease is impossible whatever is the death rate of infected mosquito.
ISSN:2331-8422