Mathematical modeling of zika virus disease with nonlinear incidence and optimal control

The Zika virus was first discovered in a rhesus monkey in the Zika Forest of Uganda in 1947, and it was isolated from humans in Nigeria in 1952. Zika virus disease is primarily a mosquito-borne disease, which is transmitted to human primarily through the bite of an infected Aedes species mosquito. H...

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Bibliographic Details
Published in:Journal of physics. Conference series 2018-04, Vol.1000 (1), p.12114
Main Authors: Goswami, Naba Kumar, Srivastav, Akhil Kumar, Ghosh, Mini, Shanmukha, B
Format: Article
Language:English
Subjects:
Mathematical models
Maximum principle
Mosquitoes
Optimal control
Physics
Viruses
Zika virus
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Summary:The Zika virus was first discovered in a rhesus monkey in the Zika Forest of Uganda in 1947, and it was isolated from humans in Nigeria in 1952. Zika virus disease is primarily a mosquito-borne disease, which is transmitted to human primarily through the bite of an infected Aedes species mosquito. However, there is documented evidence of sexual transmission of this disease too. In this paper, a nonlinear mathematical model for Zika virus by considering nonlinear incidence is formulated and analyzed. The equilibria and the basic reproduction number (R0) of the model are found. The stability of the different equilibria of the model is discussed in detail. When the basic reproduction number R0 < 1, the disease-free equilibrium is locally and globally stable i.e. in this case disease dies out. For R0 > 1, we have endemic equilibrium which is locally stable under some restriction on parameters. Further this model is extended to optimal control model and is analyzed by using Pontryagin's Maximum Principle. It has been observed that optimal control plays a significant role in reducing the number of zika infectives. Finally, numerical simulation is performed to illustrate the analytical findings.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/1000/1/012114