Analysis of a Stage-Dependent Epidemic Model Based on a Non-Markov Random Process

We present some stochastic model of an infection spread among the adult population of a certain region. The model bases on a random birth and death process supplemented by the point distributions that reflect the durations of stay of individuals at various stages of the disease. The durations of some stages of the disease are assumed constant. The model is a stochastic analog of a system of delay differential equations and convolution integral equations describing the infection spread in the deterministic approach. We address the problem of the infection eradication over a time span comparable to the average lifetime of several generations of individuals. The results of computational experiments are presented, where the dynamics of mathematical expectations of the size of certain groups of individuals is studied and the probability of the infection eradication over a finite time span is estimated using the Monte Carlo method.