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Spatiotemporal Dynamics of a Class of Models Describing Infectious Diseases

  • Khalid HattafEmail author
  • Noura Yousfi
Chapter
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 200)

Abstract

In this chapter, we propose and analyze a class of three spatiotemporal models describing infectious diseases caused by viruses such as the human immunodeficiency virus (HIV) and the hepatitis B virus (HBV). The first model with cellular immunity, the second with humoral immunity and the third with cellular and humoral immune responses. In the three proposed models, the disease transmission process is modeled by a general incidence function which includes several forms existing in the literature. In addition, the global analysis of the proposed models is rigorously investigated. Furthermore, biological findings of our analytical results are presented. Moreover, mathematical virus models and results presented in many previous studies are extended and generalized.

Keywords

Virus dynamics Immunity Diffusion Lyapunov functional Global stability 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Centre Régional des Métiers de l’Education et de la Formation (CRMEF)CasablancaMorocco
  2. 2.Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M’sikHassan II UniversitySidi Othman, CasablancaMorocco

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