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Spatiotemporal Dynamics of a Class of Models Describing Infectious Diseases

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Book cover Mathematics Applied to Engineering, Modelling, and Social Issues

Part of the book series: Studies in Systems, Decision and Control ((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.

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Author information

Authors and Affiliations

  1. Centre Régional des Métiers de l’Education et de la Formation (CRMEF), 20340 Derb Ghalef, Casablanca, Morocco

    Khalid Hattaf

  2. Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M’sik, Hassan II University, P.O Box 7955, Sidi Othman, Casablanca, Morocco

    Noura Yousfi

Authors
  1. Khalid Hattaf
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  2. Noura Yousfi
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Corresponding author

Correspondence to Khalid Hattaf .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University College London, London, UK

    Frank T. Smith

  2. Department of Mathematics, Gauhati University, Guwahati, Assam, India

    Hemen Dutta

  3. Department of Mathematics, Center for Mathematics of Uncertainty, Creighton University, Omaha, NE, USA

    John N. Mordeson

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Hattaf, K., Yousfi, N. (2019). Spatiotemporal Dynamics of a Class of Models Describing Infectious Diseases. In: Smith, F.T., Dutta, H., Mordeson, J.N. (eds) Mathematics Applied to Engineering, Modelling, and Social Issues. Studies in Systems, Decision and Control, vol 200. Springer, Cham. https://doi.org/10.1007/978-3-030-12232-4_16

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  • DOI: https://doi.org/10.1007/978-3-030-12232-4_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-12231-7

  • Online ISBN: 978-3-030-12232-4

  • eBook Packages: EngineeringEngineering (R0)

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