Mathematical Theory and Modeling
ON ESTIMATING THE CONTROL REPRODUCTION NUMBER OF ZIKA VIRUS DISEASE CONTROL MODEL
Abstract
In this paper, the possibility of stopping the spread of zika virus disease by introducing wolbachia-infected aedes aegypti mosquitoes in the zika endemic area is shown. A system of 14 nonlinear ordinary di erential equations is constructed, which models the transmission dynamics of the disease in the human and aedes aegypti populations, including the population of wolbachia-infected aedes aegypti used for control. The expression for the control reproduction number Rc was derived using the next generation matrix. Numerical evaluation of Rc at the baseline parameter values shows that Rc = 0:1206 as against the value for the basic reproduction number R0 = 1:123. This result shows that in the presence of wolbachia- infected mosquitoes, the reproduction number is reduced to below unity, which is the necessary condition for the disease eradication.
KEY WORDS: zika, aedes aegypti, wolbachia-infected mosquitoes, control reproduction number Mathematics
Subject Classication: 92B05, 00A71, 35A24
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ISSN (Paper)2224-5804 ISSN (Online)2225-0522
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