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


International Research Journal of Public Health-2D code

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


References

[1] Cristiane Wanderley Cardoso et al. _Outbreak of exanthematous illness associated with Zika, chikungunya, and dengue viruses, Salvador, Brazil_. In: (2015). doi: https: //dx.doi.org/10.3201/eid2112.151167.
[2] Wanwisa Dejnirattisai et al. _Dengue virus sero-cross-reactivity drives antibodydependent enhancement of infection with zika virus_. In: Nature immunology 17.9 (2016), p. 1102.
[3] Nuno R Faria et al. _Establishment and cryptic transmission of Zika virus in Brazil and the Americas_. In: Nature 546.7658 (2017), p. 406.
[4] Nuno Rodrigues Faria et al. _Zika virus in the Americas: early epidemiological and genetic _ndings_. In: Science 352.6283 (2016), pp. 345_349.
[5] Silvana Favoretto et al. _First detection of Zika virus in neotropical primates in Brazil: a possible new reservoir._ In: bioRxiv (2016), p. 049395.
[6] Thomas Fréour et al. _Sexual transmission of Zika virus in an entirely asymptomatic couple returning from a Zika epidemic area, France, April 2016_. In: Eurosurveillance 21.23 (2016).
[7] Daozhou Gao et al. _Prevention and control of Zika as a mosquito-borne and sexually transmitted disease: a mathematical modeling analysis_. In: Scienti_c Reports 6 (2016), p. 28070.
[8] A Gulland. WHO warns European countries to be on alert for Zika. BMJ 352, i753. 2016.
[9] Juniorcaius Ikejezie et al. _Zika virus transmission_region of the Americas, May 15, 2015_December 15, 2016_. In: American Journal of Transplantation 17.6 (2017), pp. 1681_1686.
[10] Juan Carlos Jamboos et al. _Simulation Model to the Zika Virus Considering Asymptomatic Population_. In: Open Journal of Modelling and Simulation 6.01 (2017), p. 1.
[11] M Khalid and Fareeha Sami Khan. _Stability Analysis of Deterministic Mathematical Model for Zika Virus_. In: ().
[12] Isack E Kibona and Cuihong Yang. _SIR Model of Spread of Zika Virus Infections: ZIKV Linked to Microcephaly Simulations_. In: Health 9.08 (2017), p. 1190.
[13] Adam J Kucharski et al. _Transmission dynamics of Zika virus in island populations: a modelling analysis of the 2013_14 French Polynesia outbreak_. In: PLoS Negl Trop Dis 10.5 (2016), e0004726.
[14] Oscar Arias Manrique et al. _A Simulation Model for Sexual and Vectorial Transmission of Zika Virus (ZIKV)_. In: Open Journal of Modelling and Simulation 5.01 (2016), p. 70.
[15] Jonathan J Miner et al. _Zika virus infection during pregnancy in mice causes placental damage and fetal demise_. In: Cell 165.5 (2016), pp. 1081_1091.
[16] D. Musso. _Zika virus transmission from French Polynesia to Brazil_. In: Emerg Infect Dis 21.10 (2015), p. 1887.
[17] Hiroshi Nishiura et al. _Preliminary estimation of the basic reproduction number of Zika virus infection during Colombia epidemic, 2015_2016_. In: Travel medicine and infectious disease 14.3 (2016), pp. 74_276.
[18] Joacim Rocklöv et al. _Assessing seasonal risks for the introduction and mosquitoborne spread of Zika virus in Europe_. In: EBioMedicine 9 (2016), pp. 250_256.
[19] Diana Patricia Rojas et al. _The epidemiology and transmissibility of Zika virus in Girardot and San Andres island, Colombia, September 2015 to January 2016_. In: Euro surveillance: European communicable disease bulletin 21.28 (2016).
[20] Jean Marie Turmel et al. _Late sexual transmission of Zika virus related to persistence in the semen_. In: The Lancet 387.10037 (2016), p. 2501.