Global dynamics of an epidemic model with incomplete recovery in a complex network
| Autor: | Adel Settati, Mustapha El Jarroudi, Mohamed El Fatini, Aadil Lahrouz, Hamza El Mahjour |
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| Rok vydání: | 2020 |
| Předmět: |
Lyapunov function
Series (mathematics) Computer Networks and Communications Applied Mathematics State (functional analysis) Complex network symbols.namesake Control and Systems Engineering Stability theory Signal Processing symbols Applied mathematics Uniqueness Epidemic model Heterogeneous network Mathematics |
| Zdroj: | Journal of the Franklin Institute. 357:4414-4436 |
| ISSN: | 0016-0032 |
| Popis: | In this work, we study the global dynamics of a new SIRI epidemic model with demographics, graded cure and relapse in a complex heterogeneous network. First, we analytically make out the epidemic threshold R 0 which strictly depends on the topology of the underlying network and the model parameters. Second, we show that R 0 plays the role of a necessary and sufficient condition between extinction and permanence of the disease. More specifically, by using new Lyapunov functions, we establish that the disease free-equilibrium state E0 is globally asymptotically stable when R 0 ≤ 1 , otherwise we proved the existence and uniqueness of the endemic state E*. Then, we show that E* is globally asymptotically stable. Finally, we present a series of numerical simulations to confirm the correctness of the established analytical results. |
| Databáze: | OpenAIRE |
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