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A Model for Brucellosis Disease Incorporating Age of Infection and Waning Immunity

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Listed:
  • Cyrille Kenne

    (Laboratoire LAMIA, Université des Antilles, Campus Fouillole, 97159 Pointe-à-Pitre, Guadeloupe, France
    Department of Mathematics, University of Buea, Buea 63, Cameroon)

  • Gisèle Mophou

    (Laboratoire LAMIA, Université des Antilles, Campus Fouillole, 97159 Pointe-à-Pitre, Guadeloupe, France
    Laboratoire MAINEGE, Université Ouaga 3S, Ouagadougou BP 10347, Burkina Faso)

  • René Dorville

    (Laboratoire L3MA, Unité de Formation et de Recherche Sciences Technologies Environnement (UFR STE) et Institut Universitaire de Technologie (IUT), Université des Antilles, 97275 Schoelcher, Martinique)

  • Pascal Zongo

    (Laboratoire L3MA, Unité de Formation et de Recherche Sciences Technologies Environnement (UFR STE) et Institut Universitaire de Technologie (IUT), Université des Antilles, 97275 Schoelcher, Martinique)

Abstract

This paper proposes a model for brucellosis transmission. The model takes into account the age of infection and waning immunity, that is, the progressive loss of immunity after recovery. Three routes of transmissions are considered: vertical transmission, and both direct and indirect routes of horizontal transmission. According to the well-posedness results, we provide explicit formulas for the equilibria. Next, we derive the basic reproduction number R 0 and prove some stability results depending on the basic reproductive number. Finally, we perform numerical simulations using model parameters estimated from biological data to confirm our theoretical results. The results of these simulations suggest that for certain values of parameters, there will be periodic outbreaks of epidemics, and the disease will not be eradicated from the population. Our results also highlight the fact that the birth rate of cattle significantly influences the dynamics of the disease. The proposed model can be of a good use in studying the effects of vaccination on the cattle population.

Suggested Citation

  • Cyrille Kenne & Gisèle Mophou & René Dorville & Pascal Zongo, 2022. "A Model for Brucellosis Disease Incorporating Age of Infection and Waning Immunity," Mathematics, MDPI, vol. 10(4), pages 1-19, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:670-:d:754707
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    References listed on IDEAS

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    1. Wei Zhang & Juan Zhang & Yong-Ping Wu & Li Li, 2019. "Dynamical Analysis of the SEIB Model for Brucellosis Transmission to the Dairy Cows with Immunological Threshold," Complexity, Hindawi, vol. 2019, pages 1-13, May.
    2. Lolika, Paride O. & Mushayabasa, Steady & Bhunu, Claver P. & Modnak, Chairat & Wang, Jin, 2017. "Modeling and analyzing the effects of seasonality on brucellosis infection," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 338-349.
    3. Paride O. Lolika & Steady Mushayabasa, 2018. "Dynamics and Stability Analysis of a Brucellosis Model with Two Discrete Delays," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-20, August.
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    Cited by:

    1. Yanshu Wang & Hailiang Zhang, 2023. "Dynamical Analysis of an Age-Structured SVEIR Model with Imperfect Vaccine," Mathematics, MDPI, vol. 11(16), pages 1-19, August.

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