Stochastically asymptotically stability of the multi-group SEIR and SIR models with random perturbation |
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| Authors: | Chengjun Yuan Daqing Jiang Donal O’Regan Ravi P Agarwal |
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| Institution: | 1. Department of Mathematics, Faculty of Science, South Valley University, Qena 83523, Egypt;2. Department of Mathematics, Cankaya University, Balgat, Ankara 06530, Turkey;3. Institute of Space Sciences, Magurele-Bucharest R76900, Romania;4. Department of Mathematics, Faculty of Science, Aswan University, Aswan 81528, Egypt;1. Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai 600 005 Tamil Nadu, India;2. Department of Mathematics, Government Arts College for Women, Nilakottai 624 202 Tamil Nadu, India;1. Department of Statistics and Operations Research, Faculty of Mathematics, Complutense University of Madrid, 28040 Madrid, Spain;2. Department of Mathematics, University of Athens, Panepistemiopolis, 15784 Athens, Greece;3. Faculty of Statistical Studies, Complutense University of Madrid, 28040 Madrid, Spain |
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| Abstract: | In this paper, we discuss the multi-group SEIR and SIR model with random perturbation, allowing random fluctuation around the endemic equilibrium of deterministic SEIR and SIR models. We prove that the endemic equilibriums of the two models are both stochastic asymptotically stable. In addition, the stability condition is obtained by the construction of the Lyapunov function and graph theory. Finally, numerical simulations are presented to illustrate our mathematical findings. |
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