Premium
Semi‐Markov models of epidemics over networks with time delays
Author(s) -
Ghousein Mohammad,
Moulay Emmanuel,
Coirault Patrick
Publication year - 2023
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.5989
Subject(s) - markov chain , markov process , probabilistic logic , stability (learning theory) , computer science , markov property , state (computer science) , lyapunov function , markov model , mathematics , mathematical optimization , algorithm , artificial intelligence , statistics , nonlinear system , machine learning , physics , quantum mechanics
In this article, we extend the Markov models describing the susceptible‐infected‐susceptible (SIS) epidemics over undirected networks to take into account the virus minimum incubation period and the minimum recovery period of an infected individual. We represent both periods as time delays in the states of the extended model. However, due to the addition of time delays, the process loses its Markovain property. We use the generalized semi‐Markov theory to introduce both the incubation and recovery delays to the probabilistic dynamical models. Hence, in this paper, we propose a time‐delay version of the two principal models of the SIS epidemics over undirected networks: the exact2 N − state model and the approximated N − intertwined model. Finally, using Lyapunov analysis, we give sufficient conditions that guarantee the global exponential stability of the time‐delay N − intertwined model.