Semi‐Markov models of epidemics over networks with time delays

Mohammad Ghousein (1, 2) , Emmanuel Moulay (3, 4) , Patrick Coirault (1, 2)

1 LIAS [Poitiers] - Laboratoire d'informatique et d'automatique pour les systèmes
2 A&S - Automatique et Systèmes
3 XLIM-SRI - Systèmes et Réseaux Intelligents
4 UP - Université de Poitiers = University of Poitiers

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 exact 2^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.

Mots clés: Epidemic models; semi-Markov theory; time-delay systems; multi-agent systems.

Domaines: Système multi-agents [cs.MA]; Automatique; Santé publique et épidémiologie

Mohammad Ghousein, Emmanuel Moulay, Patrick Coirault. Semi‐Markov models of epidemics over networks with time delays. International Journal of Robust and Nonlinear Control, 2023, 33 (9), pp.4761-4783. ⟨10.1002/rnc.5989⟩. ⟨hal-03511187⟩