Appl. Math. Inf. Sci. 12, No. 5, 969-982 (2018) 969 Applied Mathematics & Information Sciences An International Journal http://dx.doi.org/10.18576/amis/120510 Dynamics of Zika Virus Model with Nonlinear Incidence and Optimal Control Strategies Samson Olaniyi Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, PMB 4000 Ogbomoso, Nigeria Received: 8 Nov. 2017, Revised: 8 Aug. 2018, Accepted: 11 Aug. 2018 Published online: 1 Sep. 2018 Abstract: We formulate and analyze Zika virus transmission model with three nonlinear forces of infection from infected mosquito, asymptomatic and symptomatic humans. The sensitivity indexes of the associated parameters of the model with respect to the basic reproduction number are calculated to identify intervention strategies for prevention and control of Zika virus. Multiple time-dependent optimal controls are considered. The analysis based on the use of optimal control theory made popular by Pontryagin’s maximum principle is carried out, and the resulting optimality system is quantitatively simulated to investigate the impact of the controls on the dynamics of Zika virus. In addition, the effects of non-linearity of the forces of infection and other key parameters on the disease transmission are illustrated. Keywords: Zika virus, Basic reproduction number, Non-autonomous model, Optimal control 1 Introduction In recent times, Zika virus (ZIKV) disease has been found to be an additional source of concerns to the public health. The disease can be transmitted to humans through sexual intercourse, and primarily through an intermediate vector – infected female Aedes mosquito. According to the World Health Organization (WHO), 69 countries or territories of the world have reported mosquito-borne ZIKV transmission while 13 countries or territories have reported human-to-human transmission of ZIKV [34]. More often than not, infections with Zika are asymptomatic because only 20% of infected humans develop symptoms such as mild fever, skin rashes, conjuctivitis, muscle and joint pain [9]. The emergence of Zika virus disease in humans occurred in 1952 in Uganda and the United Republic of Tanzania. Since then, there have been several outbreaks of ZIKV in Africa, Americas, Asia and the Pacific, with the first large outbreak reported from the Island of Yap (Federated States of Micronesia) in 2007 [35]. It has been projected that Brazil among the Americas will have the largest total number of infections by more than three fold, due to a combination of its size and suitability for transmission [29]. Complications like microcephaly and Guillain-Barr´ e syndrome have been attributed to the effects of ZIKV infections while links to other neurological disorders are also being investigated ([5], [7], [22], [35]). Mathematical epidemiological models have been developed to broaden the understanding of the transmission dynamics of diseases. More importantly, the models play great roles in influencing the decision-making processes regarding intervention strategies for preventing and controlling the emergence and reemergence of the disease. A number of mathematical studies on ZIKV transmission dynamics have been carried out lately. Kucharski et al [15] used a compartmental mathematical model to examine the 2013–14 outbreak on the six major archipelagos of French Polynesia. Gao et al [11] studied a model to investigate the impact of mosquito-borne and sexual transmission on the spread and control of ZIKV. In [14], the stability analysis of infectious state of ZIKV in many types of population was presented with a view to taking necessary precautions against upcoming epidemic. Agusto et al [1] analyzed a deterministic model of ZIKV by incorporating human vertical transmission of the virus, the birth of babies with microcephaly and asymptomatically infected individuals. Padmanabhan et al [30] considered ZIKV model that incorporates both sexual and vector transmission modes with constant * Corresponding author e-mail: solaniyi@lautech.edu.ng c  2018 NSP Natural Sciences Publishing Cor.