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A Mathematical Modelling of the Effect of Treatment in the Control of Malaria in a Population with Infected Immigrants

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Abstract: In this work, we developed a compartmental bio-mathematical model tostudy the effect of treatment in the control of malaria in a population withinfected immigrants. In particular, the vector-host population model consistsof eleven variables, for which graphical profiles were provided to depict theirindividual variations with time. This was possible with the help of MathCADsoftware which implements the Runge-Kutta numerical algorithm to solvenumerically the eleven differential equations representing the vector-hostmalaria population model. We computed the basic reproduction ratio R0 following the next generation matrix. This procedure converts a system ofordinary differential equations of a model of infectious disease dynamics toan operator that translates from one generation of infectious individuals tothe next. We obtained R0 = , i.e., the square root of the product ofthe basic reproduction ratios for the mosquito and human populations respectively. R0m explains the number of humans that one mosquito can infectthrough contact during the life time it survives as infectious. R0h on theother hand describes the number of mosquitoes that are infected throughcontacts with the infectious human during infectious period. Sensitivityanalysis was performed for the parameters of the model to help us knowwhich parameters in particular have high impact on the disease transmission,in other words on the basic reproduction ratio R0.

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