Analysis of a SIRI Epidemic Model with Distributed Delay and Relapse

  • Abdelhai Elazzouzi Department of MPI, University Sidi Mouhamed Ben Abdellah, FP Taza, LSI Laboratory, Morocco
  • Abdesslem Lamrani Alaoui Department of Mathematics, University Moulay Ismaıl, FST Errachidia, M2I Laboratory, MAMCS Group, Morocco
  • Mouhcine Tilioua
  • Delfim F. M. Torres Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
Keywords: Global stability, Nonlinear incidence function, distributed delay, Lyapunov functionals, Relapse.

Abstract

We investigate the global behaviour of a SIRI epidemic model with distributed delay and relapse. From the theory of functional differential equations with delay, we prove that the solution of the system is unique, bounded, and positive, for all time. The basic reproduction number R0 for the model is computed. By means of the direct Lyapunov method and LaSalle invariance principle, we prove that the disease free equilibrium is globally asymptotically stable when R0 < 1. Moreover,we show that there is a unique endemic equilibrium, which is globally asymptotically stable, when R0 > 1.

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Published
2019-08-17
How to Cite
Elazzouzi, A., Alaoui, A. L., Tilioua, M., & Torres, D. F. M. (2019). Analysis of a SIRI Epidemic Model with Distributed Delay and Relapse. Statistics, Optimization & Information Computing, 7(3), 545-557. https://doi.org/10.19139/soic-2310-5070-831
Section
Research Articles