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Stability Analysis for a Discrete SIR Epidemic Model with Delay and General Nonlinear Incidence Function
Département de Mathématiques, UFR des Sciences et Techniques Université Nazi Boni de Bobo-Dioulasso & LAboratoire de Mathématique et d’Informatique (LAMI), Bobo-Dioulasso, Burkina Faso
Département de Mathématiques, UFR des Sciences et Techniques Université Nazi Boni de Bobo-Dioulasso & LAboratoire de Mathématique et d’Informatique (LAMI), Bobo-Dioulasso, Burkina Faso
Département de Mathématiques, UFR des Sciences et Techniques Université Nazi Boni de Bobo-Dioulasso & LAboratoire de Mathématique et d’Informatique (LAMI), Bobo-Dioulasso, Burkina Faso
- 1 Département de Mathématiques, UFR des Sciences et Techniques Université Nazi Boni de Bobo-Dioulasso & LAboratoire de Mathématique et d’Informatique (LAMI), Bobo-Dioulasso, Burkina Faso
- 2 Département de Mathématiques, UFR des Sciences et Techniques Université Nazi Boni de Bobo-Dioulasso & LAboratoire de Mathématique et d’Informatique (LAMI), Bobo-Dioulasso, Burkina Faso
- 3 Département de Mathématiques, UFR des Sciences et Techniques Université Nazi Boni de Bobo-Dioulasso & LAboratoire de Mathématique et d’Informatique (LAMI), Bobo-Dioulasso, Burkina Faso
Applied Mathematics·Volume 09 (2018)·Pages 1039–1054·Published 17 September 2018·DOI10.4236/am.2018.99070
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Abstract
In this paper, we construct a backward difference scheme for a class of SIR epidemic model with general incidence f . The step size τ used in our discretization is one. The dynamical properties are investigated (positivity and the boundedness of solution). By constructing the Lyapunov function, the general incidence function f must satisfy certain assumptions, under which, we establish the global stability of endemic equilibrium when R 0 >1. The global stability of diseases-free equilibrium is also established when R 0 ≤1. In addition we present numerical results of the continuous and discrete model of the different class according to the value of basic reproduction number R 0 .
KeywordsDiscrete ModelDelayLyapunov FunctionalNonlinear IncidenceBackward Difference SchemeLocal StabilityGlobal Stability
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