@article{Besalú2023, 
author = {Mireia Besalú and Giulia Binotto},
title = {Time-dependent non-homogeneous stochastic epidemic model of SIR type},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {10},
pages = {23218-23246},
keywords = {SIR model, basic reproduction number, epidemic model, stochastic differential equations, Markov chain},
url = {https://www.sciopen.com/article/10.3934/math.20231181},
doi = {10.3934/math.20231181},
abstract = {To better describe the spread of a disease, we extend a discrete time stochastic SIR-type epidemic model of Tuckwell and Williams. We assume the dependence on time of the number of daily encounters and include a parameter to represent a possible quarantine of the infectious individuals. We provide an analytic description of this Markovian model and investigate its dynamics. Both a diffusion approximation and the basic reproduction number are derived. Through several simulations, we show how the evolution of a disease is affected by the distribution of the number of daily encounters and its dependence on time. Finally, we show how the appropriate choice of this parameter allows a suitable application of our model to two real diseases.}
}