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

Abstract

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