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Complete global stability for an SIRS epidemic model with generalized non-linear incidence and vaccination |
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| Authors: | Aadil Lahrouz Lahcen OmariDriss Kiouach Aziza Belmaâti |
| Institution: | a Laboratory of Computer Sciences, Statistics and Quality, Department of Mathematics, Faculty of Sciences Dhar-Mehraz, B.P. 1796 Atlas, Fez, Morocco b MSTI Laboratory, High School of Technology, Ibn Zohr University, Agadir, Morocco c Laboratory of Mathematics, Cryptography and Mechanics. Faculty of Sciences and Technics, University Hassan second Mohammedia-Casablanca, B.P. 146 Mohammedia, 20650 Morocco, Morocco |
| Abstract: | This paper deals with global dynamics of an SIRS epidemic model for infections with non permanent acquired immunity. The SIRS model studied here incorporates a preventive vaccination and generalized non-linear incidence rate as well as the disease-related death. Lyapunov functions are used to show that the disease-free equilibrium state is globally asymptotically stable when the basic reproduction number is less than or equal to one, and that there is an endemic equilibrium state which is globally asymptotically stable when it is greater than one. |
| Keywords: | Epidemic model Vaccination Non-linear incidence rate Reproduction number Global stability Lyapunov function |
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