Studies on the basic reproduction number in stochastic epidemic models with random perturbations

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.

Simulation of epidemic models with generally distributed sojourn times

Epidemic models are used to analyze the progression or outcome of an epidemic under different control policies like vaccinations, quarantines, lockdowns, use of face-masks, pharmaceutical interventions, etc. When these models accurately represent real-life situations, they may become an important tool in the decision-making process. Among these models, compartmental models are very popular and assume individuals move along a series of compartments that describe their current health status. Nevertheless, these models are mostly Markovian, that is, the time in each compartment follows an exponential distribution. Here, we introduce a novel approach to simulate general stochastic epidemic models that accepts any distribution for the sojourn times.