A stochastic differential equation SIS epidemic model with two independent Brownian motions

By Siyang Cai, Yongmei Cai, Xuerong Mao. Journal of Mathematical Analysis and Applications, 2019

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Abstract In this paper, we introduce two perturbations in the classical deterministic susceptible–infected–susceptible epidemic model. Greenhalgh and Gray [4] in 2011 use a perturbation on β in SIS model. Based on their previous work, we consider another perturbation on the parameter μ + γ and formulate the original model as a stochastic differential equation (SDE) with two independent Brownian Motions for the number of infected population. We then prove that our Model has a unique and bounded global solution I ( t ) . Also we establish conditions for extinction and persistence of the infected population I ( t ) . Under the conditions of persistence, we show that there is a unique stationary distribution and derive its mean and variance. Computer simulations illustrate our results and provide evidence to back up our theory.

Subfields: Genetics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/00534c12c2c6aad04ec3d74489ec09f2afd8a342