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Studies on the basic reproduction number in stochastic epidemic models with random perturbations
Andrés Ríos-Gutiérrez1, Soledad Torres2, Viswanathan Arunachalam1
1Department of Statistics, Universidad Nacional de Colombia, Bogotá, Colombia.
Abstract:
In this paper, we discuss the basic reproduction number of stochastic epidemic models with random perturbations. We define the basic reproduction number in epidemic models by using the integral of a function or survival function. We study the systems of stochastic differential equations for SIR, SIS, and SEIR models and their stability analysis. Some results on deterministic epidemic models are also obtained. We give the numerical conditions for which the disease-free equilibrium point is asymptotically stable.
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