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SEIRS Mathematical Model for Malaria with Treatment
Mathematical Modelling and Applications
Volume 5, Issue 2, June 2020, Pages: 105-117
Received: Jan. 1, 2020; Accepted: May 5, 2020; Published: May 28, 2020
Authors
Alemu Geleta Wedajo, Department of Mathematics, Wollega University, Nekemte, Ethiopia
Purnachandra Rao Koya, Department of Mathematics, Wollega University, Nekemte, Ethiopia
Dereje Legesse Abaire, Department of Mathematics, Madda Walabu University, Bale, Robe, Ethiopia
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Abstract
In this paper a deterministic mathematical model for the spread of malaria in human and mosquito populations are presented. The model has a set of eight non – linear differential equations with five state variables for human and three for mosquito populations respectively. Susceptible humans can be infected when they are bitten by an infectious mosquito. They then progress through the exposed, infectious, treatment and recovered or immune classes before coming back to the susceptible class. Susceptible mosquitoes can become infected when they bite infectious humans, and once infected they move through exposed and infectious class. However, mosquitoes once infected will never recover from the disease during their lifetime. That is, infected mosquitoes will remain infectious until they die. Formula for the basic reproduction number R0 is established and used to determine whether the disease dies out or persists in the populations. It is shown that the disease – free equilibrium point is locally asymptotically stable using the magnitude of Eigen value and Routh – Hurwitz stability Criterion. Result and detailed discussion of the analysis as well as the simulation study is incorporated in the text of the paper lucidly.
Keywords
Dynamics of Malaria, SEIRS Model, Treatment, Local Stability, Routh – Hurwitz Criterion, Reproduction Number, Simulation Study
Alemu Geleta Wedajo, Purnachandra Rao Koya, Dereje Legesse Abaire, SEIRS Mathematical Model for Malaria with Treatment, Mathematical Modelling and Applications. Vol. 5, No. 2, 2020, pp. 105-117. doi: 10.11648/j.mma.20200502.16
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