A Stochastic Approach in the Analysis of Compartmental Models in Epidemiology (Contemporary Mathematics, 2024)
The spread of infectious diseases is a significant public health issue. Mathematical modeling is being used to find appropriate answers to this question. In this paper we propose a stochastic approach to compartmental models. A new model allows to rely on the fokker-planck equation with a SEIR model, with constant rates, to take into account the random environment in the propagation of a disease, markov and kolmogorov properties have been used in the modeling of the process. We have also determined the basic reproduction rate R0 of our new stochastic model using the new generation matrix.
Keywords: compartimental models; SEIRS; kolmogorov equation; fokker planck equation; epidemiology