2016 Deterministic Model Behind Zika Virus Infections in Brazil

2016 Deterministic Model Behind Zika Virus Infections in Brazil

Isack E. Kibona, Cuihong Yang, Shanshan Dong

College of Mathematics and Statistics, Central China Normal University, 152 Luoyu Avenue, Wuhan, Hubei 430079, P. R. China

We formulated a deterministic model for simulation of zika virus (ZIKV) infections. This cooperates with WHO serious alert on February 1st, 2016 to contain ZIKV epidemic in the world, Brazil being the most hit. Accordingly, we have taken Brazil records on ZIKV cases as an example to justify the model. According to the model, simulations suggests that by 2020, ZIKV infections is no longer a threat in this country. In our analytic analysis we have included some brief simulations as specific cases. Finally, model simulation is all about Brazil.
In this model, besides a disease free equilibrium (DFE) point being globally stable, analysis of local DFE has two sets of eigenvalues, leading two different qualitative behavior. This follows due to variation in some parameters. In each of these two sets, none has backward bifurcation. That is the disease is controllable when R_0<1. Otherwise, when R_0>1 the disease free is unstable. In the analytic analysis of either qualitative behavior, we have associated brief simulation. Only analytic analysis of endemic equilibrium has not been fully developed.
We have considered Brazil ZIKV cases from January 2016 onward to verify the model plus having some predictions about ZIKV infections to around 2020. The basic reproduction (R_0) has been estimated as R_0=0.1922<1, since then ZIKV infections has been decreasing since highest peak in early 2016. Should this value of R_0=0.1922 be stabilized or lowered, then ZIKV infections is no longer a threat in Brazil by 2020. Simulations for Brazil has been extended to understand the possible situation if R_0>1.

Keywords:Deterministic model of ZIKV infections; ZIKV simulation in Brazil; stability of DFE.

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How to cite this article:
Isack E. Kibona, Cuihong Yang, Shanshan Dong.2016 Deterministic Model Behind Zika Virus Infections in Brazil. International Research Journal of Public Health, 2018; 2:11.. DOI:10.28933/irjph-2018-06-2501


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