A two-group age of infection epidemic model with periodic behavioral changes

Mamadou L. Diagne; Ousmane Seydi; Aissata A. B. Sy

doi:10.3934/dcdsb.2019202

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2020, Volume 25, Issue 6: 2057-2092. Doi: 10.3934/dcdsb.2019202

This issue Previous Article Takens–Bogdanov singularity for age structured models Next Article The operating diagram for a model of competition in a chemostat with an external lethal inhibitor

A two-group age of infection epidemic model with periodic behavioral changes

1.
University of Thies, Senegal
2.
Polytechnic School of Thies, Senegal

^* Corresponding author: Ousmane Seydi
^* Corresponding author: Ousmane Seydi

Received: January 2019

Early access: September 2019

Published: June 2020

All the authors are supported by the CEA-MITIC (Senegal)

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Abstract

In this paper we propose a two-group SIR age of infection epidemic model by incorporating periodical behavioral changes for both susceptible and infected individuals. Our model allows different incubation periods for the two groups. It is proved in this paper that the persistence and extinction of the disease are determined by a threshold condition given in term of the basic reproductive number $ R_0 $. That is, the disease is uniformly persistent if $ R_0 >1 $ with the existence of a positive periodic solution, while the disease goes to extinction if $ R_0< 1 $ with the global asymptotic stability of the disease free periodic solution. The model we have proposed is general and can be applied to a wide class of diseases.

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Mathematics Subject Classification: Primary: 92D30, 34K20; Secondary: 34K13.

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