SIAM Journal on Applied Mathematics · 2011 · 746 citations · 17 references
Veterinary MedicineInfectious DiseasesDynamical SystemsStochastic ModelingStochastic ProcessesDisease SpreadInfectious Disease DynamicsPopulation PersistenceStochastic Differential EquationsStochastic Systems ModelingTransmission DynamicsEpidemic ModelsEpidemic Population DynamicsEpidemic Spreading ModelsMathematical Modeling Of EpidemicsModeling Of Outbreak SpreadStochastic Epidemic ModelsStochastic Noise ProcessesSusceptible-infected-susceptible Models
In this paper we extend the classical susceptible-infected-susceptible epidemic model from a deterministic framework to a stochastic one and formulate it as a stochastic differential equation (SDE) for the number of infectious individuals $I(t)$. We then prove that this SDE has a unique global positive solution $I(t)$ and establish conditions for extinction and persistence of $I(t)$. We discuss perturbation by stochastic noise. In the case of persistence we show the existence of a stationary distribution and derive expressions for its mean and variance. The results are illustrated by computer simulations, including two examples based on real-life diseases.
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