A mathematical model of Zika virus transmission with saturated incidence and optimal control: A case study of 2016 zika outbreak in Puerto Rico

References

• Lakshmikantham V, Leela S, Martynyuk AA. Stability Analysis of Nonlinear System. New York and Basel: Marcel Dekker. Inc; 1989.
   Google Scholar
• Esteva L, Vargas C. Influence of vertical and mechanical transmission on the dynamics of dengue disease. Math Biosci. 2000;167:51–64.
   PubMed Web of Science ®Google Scholar
• Agusto FB, Khan MA. Optimal Control Strategies for Dengue Transmission in Pakistan. Math Biosci. 2018;305:102–121.
   PubMed Web of Science ®Google Scholar
• Rasmussen SA, Jamieson DJ, Honein MA, et al. Zika virus and birth defects reviewing the evidence for casuality. New Engl Med. 2016;374(20):1981–1987.
   PubMed Web of Science ®Google Scholar
• McGrath EL, Rossi SL, Gao J, et al. Differntial responses of human fetal brain neural stem cells to Zika virus infection. Stem Cell Rep. 2017;8(3):715–727.
   PubMed Web of Science ®Google Scholar
• Charnig K, Cucunuba ZN, Walteros DM, et al. Descriptive analysis of surveillance data for Zika virus disease and Zika virus associated neurological complications in Colombia, 2015-2017. PLoS ONE. 2021 Jun 16; 16(6):e0252236.
   PubMed Web of Science ®Google Scholar
• Sharma V, Sharma M, Dhull D, et al. Zika virus: an emerging challenge to public health worldwide. Can J Microbiol. 2020 Feb 2; 66:87–98
   PubMed Web of Science ®Google Scholar
• Parra B, Lizaarazo J, Jimenez-Arango JA, et al. Guillain-Barre syndrome associated with Zika virus infection in Colombia. New Engl J Med. 2016;375(16):1513–1523.
   PubMed Web of Science ®Google Scholar
• Brouter N, Krauer F, Riesen M, et al. Zika virus as a cause of neurologic disorders. New Engl J Med. 2016;374(16):1506–1509.
   PubMed Web of Science ®Google Scholar
• Brooks JT, Friedman A, Kachur RE, et al. Update: interim guidance for prevention of sexual transmission of zika virus-United States. 2016. MMWR Morb Mortal Wkly Rep. 2016 July;65(29):745.
   PubMed Web of Science ®Google Scholar
• Petersen EE, Meaney-Delman D, Neblett-Fanfair R, et al. Update: interim guidance for preconception counselling and prevention of sexual transmission of zika virus for persons with possible zika virus exposure-United States. 2016. MMWR Morb Mortal Wkly Rep. 2016 September;65(39):1077.
   PubMed Web of Science ®Google Scholar
• Davidson A, Slavinski S, Komoto K, et al. Suspected female-to-male sexual transmission of zika virus-New York City, 2016. MMWR Morb Mortal Wkly Rep. 2016;65(28):716.
   PubMed Web of Science ®Google Scholar
• Kucharski AJ, Funk S, Eggo RM, et al. Transmission dynamics of Zika virus in Island population: a modelling analysis of the 2013-2014 French Polynesia outbreak. PLoS Negl Trop Dis. 2016;10(5):2016.
   Web of Science ®Google Scholar
• Imran M, Usman M, Dur-e-Ahmad M, et al. Transmission Dynamics of Zika Fever: a SEIR Based Model. Differ Equ Dyn Syst. 2017;28(4):791–805.
   PubMed Web of Science ®Google Scholar
• Adamu G, Bawa M, Jiya M, et al. A mathematical model for the dynamics of Zika virus via Homotopy perturbation method. J Appl Sci Environ Manage. 2017;21(4):615–623.
   Google Scholar
• Sikka V, Chattu VK, Popli RK. The emergence of zika virus as global health security threat: a new and a consensus statement of the INDUSEM Joint Working Group (JWG). Journal of Global Diseases. 2016;8(1):3–15.
   PubMed Web of Science ®Google Scholar
• World Health Organization-WHO. 2016. Zika Virus. https://www.who.int/news-room/fact-sheets/detail/zika-virus
   Google Scholar
• Biswas SK, Ghosh U, Sarkar S. Mathematical model of zika virus dynamics with vector control and sensitivity analysis.Infectious Disease Modelling. Infectious Disease Modelling. 2020;5:23–41.
   PubMedGoogle Scholar
• Agusto FB, Bewick S, Fagan WF. Mathematical model for Zika virus dynamics with Sexual transmission route. Ecol Complexity. 2017a;29:61–81.
   Web of Science ®Google Scholar
• Yuan X, Lou Y, He D, et al. A Zika Endemic Model for the Contribution of Multiple Transmission Routes. Bull Math Biol. 2021;83:111.
   PubMed Web of Science ®Google Scholar
• Ibrahim M, Denes A. A: threshold Dynamics in a Model for Zika Virus Disease with Seasonality. Bull Math Biol. 2021;83:27.
   PubMed Web of Science ®Google Scholar
• Denes A, Ibrahim MA, Oluoch L, et al. Impact of weather seasonality and sexual transmission on the spread of Zika fever. Sci Rep. 2019;9:17055.
   PubMed Web of Science ®Google Scholar
• Rahman M, Bekele-Maxwell K, Cates LL, et al. Modeling Zika Virus Transmission Dynamics: parameter Estimates, Disease Characteristics, and Prevention. Sci Rep. 2019;9:10575.
   PubMed Web of Science ®Google Scholar
• Khan MA, Shah SW, Ullah S, et al. A dynamical model of asymptomatic carrier zika virus with optimal control strategies. Nonlinear Analysis: Real World Applications. 2019;50:144–170.
   Web of Science ®Google Scholar
• Alzahrani EO, Ahmad W, Khan MA, et al. Optimal control strategies of Zika virus model with mutant. Comm Nonlinear Science and Numerical Simulation. 2021;93:105532.
   Web of Science ®Google Scholar
• Olaniyi S. Dynamics of Zika virus model with non-linear incidence and optimal control strategies. Appl Math Inf Sci. 2018;12(5):969–982.
   Google Scholar
• Bonyah E, Khan MA, Okosun KO, et al. A.: theoretical Model for Zika virus transmission. PLOS ONE. 2017;12(10):e0185540.
   PubMed Web of Science ®Google Scholar
• Shah NH, Patel ZA, Yeolekar BM. Prevention and controls on congenital transmissions of Zika: mathematical Analysis. Appl Math. 2017;8:500–519.
   Google Scholar
• Ali A, Iqbal Q, Kiddy J, et al. Mathematical modeling for the transmission potential of Zika virus with optimal control strategies. Eur Phys J Plus. 2022;137:146.
   Web of Science ®Google Scholar
• Ukanwoke NO, Okuonghae D, Inyama SC. Modelling the dynamics of Zika in a population with two strains of the virus with optimal control and cost-effectiveness analysis. Int J Dynam Control. 2021. DOI:10.1007/s40435-021-00856-7
   Web of Science ®Google Scholar
• Srivastav AK, Goswami NK, Ghosh M. Modeling and optimal control analysis of Zika virus with media impact. Int J Dynam Control. 2018;6:1673–1689.
   Google Scholar
• Okyere E, Olaniyi S, Bonyah E. Analysis of Zika virus dynamics with sexual transmission route using multiple optimal controls. Sci Afr. 2020;9. DOI:10.1016/j.sciaf.2020.e00532
   Google Scholar
• Capasso V, Serio G. A generalization of the Kermack-Mckendrick deterministic epidemic model. Math Biosci. 1978;42(1–2):43–61.
   Web of Science ®Google Scholar
• Hethcote HW. : the mathematics of infectious diseases. SIAM Rev. 2000;42(4):599–653.
   Web of Science ®Google Scholar
• Van den Driessche P, Watmough J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math Biosci. 2002;180:29–48.
   PubMed Web of Science ®Google Scholar
• Shuai Z, Vanden Driessche P. Global stability of infectious disease models using Lyapunov functions. SIAM J Appl Math. 2013;73(4):1513–1532.
   Web of Science ®Google Scholar
• Hethcote HW, Thieme HR. Stability of the endemic equilibrium in epidemic models with subpopulations. Math Biosci. 1985;75:205–227.
   Web of Science ®Google Scholar
• PAHO/WHO Data-weekly report. [cited 2021 Jan 31]. https://www.paho.org/data/index.php/en/mnu-topics/zika/524-zika-weekly-en.html
   Google Scholar
• Demographics of Puerto Rico-wikipediaen. [cited 2021 Jan 31]. https://wikipedia.org/wiki/Demographics-of-Puerto-Rico
   Google Scholar
• Massad E, Coutinho FAB, Burattini M, et al. The risk of yellow fever in a dengue-infested area. Trans R Soc Trop Med Hyg. 2001;95:370–374.
   PubMed Web of Science ®Google Scholar
• Favier C, Degallier N, Rosa-Freitas MG. Early determination of the reproductive number of vector-borne diseases: the case of dengue in Brazil. Trop Med Int Health. 2006;11:332–340.
   PubMed Web of Science ®Google Scholar
• Pinho S, Ferreira C, Esteva L, et al. Modelling the dynamics of dengue real epidemics. Phil Trans R Soc, A. 2010;368:5679–5692.
   Web of Science ®Google Scholar
• Nishiura H, Chowell G. The effective reproduction number as aprelude to statistical estimation of time-dependent epidemic trends. In Mathematical and statistical estimation approaches in epidemiology. New York: Springer; 2009. p.103–121.
   Google Scholar
• Wallinga J, Lipsitch M:. How generation intervals shape the relationship between growth rates and reproductive numbers. Proceedings of the Royal Society B: Biological Sciences. 2007;274(1609):599–604.
   PubMed Web of Science ®Google Scholar
• Chitnis N, Hyman JM, Cushing JM. : determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model. Bull Math Biol. 2008;70(5):1272–1296.
   PubMed Web of Science ®Google Scholar
• Pontryagin LS, Boltyanskii VG, Gamkrelidze RV, et al. The Mathematical Theory of Optimal Process. Vol. 4. New York: Gordon and Breach science Publishers; 1986.
   Google Scholar
• Olaniyi S, Mukamuri M, Okosun KO, et al. Mathematical analysis of a social hierarchy-structured model for malaria transmission dynamics. Results Phys. 2022;34. DOI:10.1016/j.rinp.2021.104991
   Web of Science ®Google Scholar
• Abimbade SF, Olaniyi S, Ajala OA, et al. Optimal control analysis of a tuberculosis model with exogenous re-infection and incomplete treatment. Optim Control Applications and Methods. 2020;41(6):2349–2368.
   Web of Science ®Google Scholar
• Carvalho SA, da Silva SO, da Cunha IC. Mathematical modeling of dengue epidemic: control methods and vaccination strategies Theory in Biosciences. 2015;138.2(2019):223–239.
   Google Scholar
• Falowo OD, Olaniyi S, Oladipo AT. Optimal control assessment of Rift Valley fever model with vaccination and environmental sanitation in the presence of treatment delay. Model Earth Syst Environ. 2022. 10.1007/s40808-022-01508-1
   Web of Science ®Google Scholar
• Olaniyi S, Falowo OD, Okosun KO, et al. Effect of saturated treatment on malaria spread with optimal intervention. Alexandria Eng J. 2022. 10.1016/j.aej.2022.09.024
   Web of Science ®Google Scholar