Optimal control in a model for Zika transmission with stratification by sex

Authors

DOI:

https://doi.org/10.17268/sel.mat.2020.02.11

Keywords:

Model, sexual transmission, strategy, optimal control, Zika

Abstract

This paper presents an optimal control strategy for the Zika virus disease with sexual transmission. A mathematical model for the transmission of the Zika virus is considered with three preventive measures as control, namely: the prevention of the sexual contagion with the use of condoms and the orientation in the transmission of Zika in the homosexual and heterosexual relations, the campaigns against vectors and the protection of the society regarding the contagion by mosquito bites. We examine the implementation of various combinations of the control strategies in order to determine the most cost-effective one. The necessary conditions for the optimal controls are determined using Pontryaguin’s maximum principle and the optimality problem is solved using Runge-Kutta fourth order scheme. Based on the computational results, we conclude that the most efficient control strategy is when it is applied on the infections in homosexual relationships combined with the control in the transmission by vectors.

Author Biographies

Erick Manuel Delgado Moya, IME- University of Sao Paulo, Rua do Matao, 1010, SP-Brazil.

Position PhD

Aymee Marrero Severo, MATCOM- University of Havana, Edificio Felipe Poey. San Lázaro y L. Colina Universitaria, Havana-Cuba.

Profesora Titular

References

Dick GWA, Kitchen SF, Haddow AJ. Zika virus (II). Pathogenicity and physical properties. Trans R Soc Trop Med Hyg. 1952; 46:521-534. DOI: 10.1016/0035-9203(52)90043-6.

Oluyo TO, Adeyemi MO. Mathematical analysis of Zika epidemic model. IOSR-JM. 2017; 12(6):21-33.

Tiemi TT, Maidan NA, Ferreira JR WC, Paulino P, Yang H. Mathematical models for the aedes aegypti dispersal dynamics: Travelling waves by wing and wind. Bull. of Math. Biology. 2005; 67:509-528.

Shutt DP, Manore CA, Pankavich S, Porter AT, Del Valle SY. Estimating the reproductive number, total outbreak size, and reporting rates for ZIKA epidemics in South and Central America. Epidemics. 2017; 21:63-79. DOI: 1710.1016/j.epidem.2017.06.005.

Duffy MR, Chen TH, Haddow WT, Powers AM, Kool JL, Lan-Gotti RS, Pretrick M, Martez M, Holzbauer S, Dubray C, et al. Zika virus outbreak on Yap Island, Federated States of Micronesia. N. Engl. J. Med. 2009; 360:2536–2543.

World Health Organization. Zika virus–Fact sheet. 2016. [Retrieved nov. 21, 2019.] Online available at http://goo.gl/fFiiuo.

Lenhart S, Workman JT. Optimal Control Applied to Biological Models. Boca Raton: CRC Press. 2007. DOI: 10.1201/9781420011418.

Fleming WH, Rishel RW. Deterministic and stochastic optimal control. New York: Springer Verlag; 1975. DOI: 10.1002/zamm.19790590940.

Jung E, Lenhart S, Feng Z. Optimal Control of treatments in a two-strain tuberculosis model. Discrete and Cont. Dyn. Syst. Serie B. 2002; 2(4):473. DOI: 10.3934/dcdsb.2002.2.473.

Fleming WH, Rishel RW. Deterministic and stochastic optimal control. New York: Springer Verlag; 1975. DOI: 10.1002/zamm.19790590940.

Gupta N, Rink R. Optimum control of epidemics. Math. Biosci. 1973; 18(3-4):383-396. DOI: 10.1016/0025-5564(73)90012-6.

Lashari AA, Zaman G. Optimal control of a vector borne disease with horizontal transmission. Nonlinear Anal. Real World Appl. 2012; 13(1):203-212. DOI: 10.1016/j.nonrwa.2011.07.026.

Rodrigues HS, Monteiro MTT, Torres DF. Vaccination models and optimal control strategies to dengue. Math. Biosci. 2014; 247:1-12. DOI: 10.1016/j.mbs.2013.10.006.

Moulay D, Aziz-Alaoui M, Kwon H-D. Optimal control of chikungunya disease: larvae reduction, treatment and prevention. Math. Biosci. Eng. 2012; 9(2):369-392. DOI: 10.3934/mbe.2012.9.369.

Kirschner D, Lenhart S, Serbin S. Optimal control of the chemotherapy of HIV. J. Math. Biol. 1997; 35(7):775-792. DOI: 10.

/ s002850050076.

Downloads

Published

2020-12-25

How to Cite

Delgado Moya, E. M., & Marrero Severo, A. (2020). Optimal control in a model for Zika transmission with stratification by sex. Selecciones Matemáticas, 7(02), 289-301. https://doi.org/10.17268/sel.mat.2020.02.11

Issue

Vol. 7 No. 02 (2020): August - December

Section

Articles

License

The authors who publish in this journal accept the following conditions:
1. The authors retain the copyright and assign to the journal the right of the first publication, with the work registered with the Creative Commons Attribution License,Atribución 4.0 Internacional (CC BY 4.0) which allows third parties to use what is published whenever they mention the authorship of the work And to the first publication in this magazine.
2. Authors may make other independent and additional contractual arrangements for non-exclusive distribution of the version of the article published in this journal (eg, include it in an institutional repository or publish it in a book) provided they clearly state that The paper was first published in this journal.
3. Authors are encouraged to publish their work on the Internet (for example, on institutional or personal pages) before and during the review and publication process, as it can lead to productive exchanges and to a greater and more rapid dissemination Of the published work.