Mathematical Model for the Dynamics of Measles under the Combined Effect of Vaccination and Measles Therapy

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Author(s) Christopher Obumneke | Ibrahim Isa Adamu | Shamaki Timothy Ado
Pages 862-874
Volume 6
Issue 6
Date June, 2017
Keywords Disease-Free Equilibrium, Infectious Disease, Jacobian Matrix, Reproduction Number, Vaccination, Dynamics, Population

The most important factor in the control of the spread of infectious disease is to understand the dynamics of the disease in a population; we can then develop strategies for the control of the disease. Available literature showed that; most authors worked on mathematical models for the dynamics of measles under the influence of Vaccination or other forms of therapies separately at the exposed class. In this work, we developed a mathematical model for the dynamics of measles under the combined effect of vaccination at the susceptible class, and administering measles drug therapy to screened infected individuals in the exposed class. In developing the model, we adopted compartmental modeling approach, where we partition the population into; Susceptible, Vaccinated, Exposed, Infected and Recovered subpopulations. The result of the model analysis showed that the model has a unique disease-free equilibrium which is locally asymptotically stable whenever the basic reproduction number, is less than one ( ˂ 1). We also carried out numerical experiment using data from Momoh et al. (2013), the results of the numerical experiments revealed that eradicating measles is more efficient if susceptible individuals are vaccinated and followed by drug therapy to screened infected individuals in the exposed class.

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