Affiliation:
1. Department of Mathematics, Faculty of Science, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia
2. ENIT-LAMSIN, Tunis El Manar University, BP. 37, Tunis-Belvédère, Tunis 1002, Tunisia
Abstract
Infectious diseases include all diseases caused by the transmission of a pathogenic agent such as bacteria, viruses, parasites, prions, and fungi. They, therefore, cover a wide spectrum of benign pathologies such as colds or angina but also very serious ones such as AIDS, hepatitis, malaria, or tuberculosis. Many epidemic diseases exhibit seasonal peak periods. Studying the population behaviours due to seasonal environment becomes a necessity for predicting the risk of disease transmission and trying to control it. In this work, we considered a five-dimensional system for a fatal disease in a seasonal environment. We studied, in the first step, the autonomous system by investigating the global stability of the steady states. In a second step, we established the existence, uniqueness, positivity, and boundedness of a periodic orbit. We showed that the global dynamics are determined using the basic reproduction number denoted by R0 and calculated using the spectral radius of an integral operator. The global stability of the disease-free periodic solution was satisfied if R0<1, and we show also the persistence of the disease once R0>1. Finally, we displayed some numerical investigations supporting the theoretical findings, where the trajectories converge to a limit cycle if R0>1.
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
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