Ergodic stationary distribution and disease eradication in a stochastic SIR model with telegraph noises and Lévy jumps

In this work, we present analysis of a SIR model where white noises, telegraph noises (Markov switching) and Lévy jumps serve as sources of environmental perturbations in the system. Based on the Feller property, we derive sufficient conditions for the existence of a unique stationary distribution w...

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Bibliographic Details
Published inInternational journal of dynamics and control Vol. 10; no. 6; pp. 1778 - 1793
Main Author Okuonghae, D.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2022
Springer Nature B.V
Subjects
Complexity
Control
Control and Systems Theory
Dynamical Systems
Engineering
Ergodic processes
Markov processes
Mathematical models
Perturbation
Switching
Vibration
Mutually exclusive probabilities
Ergodicity
Disease eradication
Stationary distribution
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Summary:In this work, we present analysis of a SIR model where white noises, telegraph noises (Markov switching) and Lévy jumps serve as sources of environmental perturbations in the system. Based on the Feller property, we derive sufficient conditions for the existence of a unique stationary distribution with ergodic property using the mutually exclusive probabilities technique (Stenner in the existence and uniqueness of invariant measure for continuous-time Markov process, Tech. Report, pp 18-86, Brown University, Providence, RI, USA, 1986). Further, in a special case, we derived condition for disease eradication. Using numerical simulations, we were able to illustrate the analytical results obtained herein. Some of the results reveal that, in a Markovian switching regime, white noises and Lévy jumps could determine whether the disease is eradicated or not, with both sources of random perturbations affecting the degree of disease persistence.
ISSN:2195-268X
2195-2698
DOI:10.1007/s40435-022-00962-0