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Mathematical modelling of Zika virus as a mosquito-borne and sexually transmitted disease with diffusion effects

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  • Hasan, Bushra
  • Singh, Manmohan
  • Richards, David
  • Blicblau, Aaron

Abstract

Zika virus disease is an infection transmitted primarily by Aedes mosquitoes, and can be a serious epidemic if not contained and controlled in its early stages. The purpose of this study is to investigate the transmission dynamics of Zika virus epidemic. A mathematical model of Zika virus with the inclusion of diffusion in the system is formulated, using a system of ordinary differential equations. Mathematical models assume transmission of the virus by mosquitoes, with and without transmission through sexual contact by humans. The basic properties of the model in the absence and presence of diffusion are determined including, points of the disease-free equilibrium (DFE) and the endemic equilibrium (EE). Stability of the disease-free equilibrium using the reproduction number, R0 is established. The stability of the endemic equilibrium is established using the Routh–Hurwitz stability conditions. Bifurcation values for transmission rates and human recovery rate are also calculated. Numerical simulations based on different population distributions help to understand how the diffusion of human and mosquitoes affects the transmission of the disease.

Suggested Citation

  • Hasan, Bushra & Singh, Manmohan & Richards, David & Blicblau, Aaron, 2019. "Mathematical modelling of Zika virus as a mosquito-borne and sexually transmitted disease with diffusion effects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 56-75.
    • Handle: RePEc:eee:matcom:v:166:y:2019:i:c:p:56-75
    DOI: 10.1016/j.matcom.2019.04.007
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    References listed on IDEAS

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    1. Ebenezer Bonyah & Muhammad Altaf Khan & K O Okosun & Saeed Islam, 2017. "A theoretical model for Zika virus transmission," PLOS ONE, Public Library of Science, vol. 12(10), pages 1-26, October.
    2. Abid Ali Lashari & Shaban Aly & Khalid Hattaf & Gul Zaman & Il Hyo Jung & Xue-Zhi Li, 2012. "Presentation of Malaria Epidemics Using Multiple Optimal Controls," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-17, June.
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    Cited by:

    1. Raja, Muhammad Asif Zahoor & Mehmood, Ammara & Ashraf, Sadia & Awan, Khalid Mahmood & Shi, Peng, 2022. "Design of evolutionary finite difference solver for numerical treatment of computer virus propagation with countermeasures model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 409-430.
    2. Sharma, Naveen & Singh, Ram & Singh, Jagdev & Castillo, Oscar, 2021. "Modeling assumptions, optimal control strategies and mitigation through vaccination to Zika virus," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).

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