Modeling metapopulation dynamics of HIV epidemic on a linear lattice with nearest neighbour coupling

  • Authors

    • Titus Rotich Moi UniversityP.O. BOX 3900 - 30100ELDORET - KENYA
    • Robert Cheruiyot South Eastern Kenya University, P.O. Box 170, Kitui
    • Pauline Anupi Kisii University, P.O. Box 408-40200, KISII
    • Flomena Jeptanui University of Eldoret, P.O. Box 1125, Eldoret
    2016-03-02
    https://doi.org/10.14419/ijamr.v5i1.5544
  • Coupling Strength, Isolation, Metapopulation, Reproductive ratio, Synchronization.

  • Abstract

    Many mathematical models for the spread of infectious diseases in a population assume homogeneous mixing, but due to spatial distribution, there exist distinct patches with unique disease dispersion dynamics, especially if between patch mixing due to travel and migration is limited. In this paper, three levels of disease status in a - patch metapopulation was studied using a simple SIR-HIV epidemic model in a one dimensional nearest neighbour coupling lattice. The basic reproductive ratio , which is a function of coupling strength , is shown to affect stability characteristics of equilibrium points. The disease free equilibrium (DFE) is globally asymptotically stable irrespective of the value of  but the stability of the endemic equilibrium point (EEP) depends on the coupling strength . It was found that at the critical value of coupling strength , the subpopulations dynamics are synchronized while for  the subpopulation dynamics are independent. Patch isolation strategy for the control of HIV dispersion requires a critical coupling strength of . This interaction restriction reduces  to values less than one, and the disease will be eliminated, making isolation effective. Demographic and epidemiological parameters of Vihiga County in Kenya were used in the study.

    Author Biography

    • Titus Rotich, Moi UniversityP.O. BOX 3900 - 30100ELDORET - KENYA

      Head of Subject

      Mathematics Department

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  • How to Cite

    Rotich, T., Cheruiyot, R., Anupi, P., & Jeptanui, F. (2016). Modeling metapopulation dynamics of HIV epidemic on a linear lattice with nearest neighbour coupling. International Journal of Applied Mathematical Research, 5(1), 73-83. https://doi.org/10.14419/ijamr.v5i1.5544

    Received date: 2015-11-15

    Accepted date: 2016-01-28

    Published date: 2016-03-02