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Mathematical Modeling and Stability Analysis of HIV with Contact Tracing According to the Changes in the Infected Classes

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4th International Conference on Computational Mathematics and Engineering Sciences (CMES-2019) (CMES 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1111))

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Abstract

In this paper, we investigate the effect of contact tracing the spread of HIV in a population. The mathematical model is given as a system of differential equations with piecewise constant arguments, where we divide the population into three sub-classes: HIV negative, HIV positive that do not know they are infected and the class with HIV positive that know they are infected. This system is analyzed using the theory of differential and difference equations. The local stability of the positive equilibrium point is investigated by using the Schur-Cohn Criteria, while for the global stability we consider an appropriate Lyapunov function. The system under consideration has shown that it has semi-cycle behaviors, but not a structure of period two. Moreover, we analyze the case for low infection rate by using the Allee effect at time t. Several examples are presented to support our theoretical findings using data from a case study in India.

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Authors and Affiliations

  1. Department of Mathematics, Kuwait College of Science and Technology, 27235, Kuwait City, Kuwait

    Ali Yousef & Fatma Bozkurt Yousef

  2. Faculty of Education, Department of Mathematics and Science Education, Erciyes University, 38039, Kayseri, Turkey

    Fatma Bozkurt Yousef

Authors
  1. Ali Yousef
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  2. Fatma Bozkurt Yousef
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Corresponding author

Correspondence to Ali Yousef .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Gauhati University, Guwahati, India

    Hemen Dutta

  2. FSTE, Moulay Ismail University, Meknes, Morocco

    Zakia Hammouch

  3. Department of Mathematics, Fırat University, Elâzığ Merkez, Turkey

    Hasan Bulut

  4. Faculty of Education, Department of Mathematics and Science Education, Harran University, Sanliurfa, Turkey

    Haci Mehmet Baskonus

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Yousef, A., Yousef, F.B. (2020). Mathematical Modeling and Stability Analysis of HIV with Contact Tracing According to the Changes in the Infected Classes. In: Dutta, H., Hammouch, Z., Bulut, H., Baskonus, H. (eds) 4th International Conference on Computational Mathematics and Engineering Sciences (CMES-2019). CMES 2019. Advances in Intelligent Systems and Computing, vol 1111. Springer, Cham. https://doi.org/10.1007/978-3-030-39112-6_2

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  • DOI: https://doi.org/10.1007/978-3-030-39112-6_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-39111-9

  • Online ISBN: 978-3-030-39112-6

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