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Asymptotic dynamics of deterministic and stochastic epidemic models with multiple pathogens. (English) Zbl 1080.34033
The paper deals with mathematical models of deterministic and stochastic multiple-stain epidemic, parts of which have reported in the literature. This work consists largely of two-strain epidemic models; the feature of such model is that the population is subdivided into susceptible individuals and individuals infected with two pathogens.
The equations for the deterministic epidemic form a system of ordinary – and for the stochastic epidemic as a system of stochastic differential equations. The models assume that there are total cross immunity, vertical transmission and a density-dependent death rate. The impact of vertical transmission on the coexistence of two strains is analyzed and the dynamics of the deterministic and stochastic model are compared. For example, it can be seen that the coexistence dynamics is different for the deterministic and stochastic models.
A set of numerical examples are given to prove the data for comparison.

MSC:
34C60 Qualitative investigation and simulation of ordinary differential equation models
34D05 Asymptotic properties of solutions to ordinary differential equations
34F05 Ordinary differential equations and systems with randomness
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
92D30 Epidemiology
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