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The Impact of Infective Immigrants on the Spread and Dynamics of Zika Viruss
American Journal of Applied Mathematics
Volume 5, Issue 6, December 2017, Pages: 145-153
Received: May 9, 2017; Accepted: May 27, 2017; Published: Nov. 5, 2017
Authors
Molalegn Ayana, School of Mathematical and Statistical Sciences, Hawassa University, Hawassa, Ethiopia
Purnachandra Rao Koya, School of Mathematical and Statistical Sciences, Hawassa University, Hawassa, Ethiopia
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Abstract
In this paper, a compartment model has been built, presented and investigated the dynamics and spread of zika virus in both human and mosquito populations. It is focused to study the impact of symptomatic and asymptomatic infective immigrants on the spread of zika virus. A new mathematical model SI1I2R for human and SI model for vector population has been designed and presented. Here I1 is symptomatic infective and I2 is asymptomatic infective human populations. The present model is developed making some reasonable modifications in the corresponding epidemic SIR model by considering symptomatic and asymptomatic infective immigrants. Susceptible vectors get infection either from symptomatic or asymptomatic infected human populations. The basic reproduction number is derived using the next generation matrix method. Disease free equilibrium point is found and endemic equilibrium state is identified. It is shown that the disease free equilibrium point is locally and globally asymptotically stable if the reproduction number takes a value less than one unit and unstable if it is more than one unit. Simulation study is conducted using MATLAB ode45.
Keywords
SI1I2R Model, Symptomatic Infected, Asymptomatic Infected, Zika Virus, Microcephally
Molalegn Ayana, Purnachandra Rao Koya, The Impact of Infective Immigrants on the Spread and Dynamics of Zika Viruss, American Journal of Applied Mathematics. Vol. 5, No. 6, 2017, pp. 145-153. doi: 10.11648/j.ajam.20170506.11
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