@Article{IJNAM-2-329,
author = {Allen , L. J. S. and Kirupaharan , N.},
title = {Asymptotic Dynamics of Deterministic and Stochastic Epidemic Models with Multiple Pathogens},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2005},
volume = {2},
number = {3},
pages = {329--344},
abstract = {<p style="text-align: justify;">Emerging diseases in animals and plants have led to much
research on questions of evolution and persistence of pathogens. In
particular, there have been numerous investigations on the evolution of
virulence and the dynamics of epidemic models with multiple pathogens.
Multiple pathogens are involved in the spread of many human diseases
including influenza, HIV-AIDS, malaria, dengue fever, and hantavirus
pulmonary syndrome [9, 15, 16, 23, 24, 27]. Understanding the impact of
these various pathogens on a population is particularly important for
their prevention and control. W summarize some of the results that have
appeared in the literature on multiple pathogen models. Then we study
the dynamics of a deterministic and a stochastic susceptible-infected
epidemic model with two pathogens, where the population is subdivided
into susceptible individuals and individuals infected with pathogen $j$ for $j = 1, 2$. The deterministic model is a system of ordinary
differential equations, whereas the stochastic model is a system of
stochastic differential equations. The models assume total cross
immunity and vertical transmission. The conditions on the parameters for
coexistence of two pathogens are summarized for the deterministic model.
Then we compare the coexistence dynamics of the two models through
numerical simulations. We show that the deterministic and stochastic
epidemic models differ considerably in predicting coexistence of the two
pathogens. The probability of coexistence in the stochastic epidemic
model is very small. Stochastic variability results in extinction of at
least one of the strains. Our results demonstrate the importance of
understanding the dynamics of both the deterministic and stochastic
epidemic models.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/934.html}
}