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A Mathematical Model to Control the Prevalence of a Directly and Indirectly Transmitted Disease

Author

Listed:
  • Begoña Cantó

    (Institut de Matemàtica Multidisciplinar, Universitat Politècnica de València, 46071 València, Spain)

  • Carmen Coll

    (Institut de Matemàtica Multidisciplinar, Universitat Politècnica de València, 46071 València, Spain)

  • Maria Jesús Pagán

    (Grupo de Investigación e Innovación Alimentaria, Universitat Politècnica de València, 46071 València, Spain)

  • Joan Poveda

    (Grupo de Investigación e Innovación Alimentaria, Universitat Politècnica de València, 46071 València, Spain)

  • Elena Sánchez

    (Institut de Matemàtica Multidisciplinar, Universitat Politècnica de València, 46071 València, Spain)

Abstract

In this paper, a mathematical model to describe the spread of an infectious disease on a farm is developed. To analyze the evolution of the infection, the direct transmission from infected individuals and the indirect transmission from the bacteria accumulated in the enclosure are considered. A threshold value of population is obtained to assure the extinction of the disease. When this size of population is exceeded, two control procedures to apply at each time are proposed. For each of them, a maximum number of steps without control and reducing the prevalence of disease is obtained. In addition, a criterion to choose between both procedures is established. Finally, the results are numerically simulated for a hypothetical outbreak on a farm.

Suggested Citation

  • Begoña Cantó & Carmen Coll & Maria Jesús Pagán & Joan Poveda & Elena Sánchez, 2021. "A Mathematical Model to Control the Prevalence of a Directly and Indirectly Transmitted Disease," Mathematics, MDPI, vol. 9(20), pages 1-15, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:20:p:2562-:d:655054
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    References listed on IDEAS

    as
    1. Li, Xiuying & Wang, Wendi, 2005. "A discrete epidemic model with stage structure," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 947-958.
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