Optimal control of Zika virus infection by vector elimination, vector-to-human and human-to-human contact reduction

Abstract

The recent outbreak of mosquito-borne Zika virus (ZIKV) in Brazil, with estimated cases surpassing 1.5 million, has gained attention due to its rapid spread and neurological complications associated with the infection such as microcephaly and Guillain-Barré syndrome. Beside vector transmission, primarily via Aedes mosquitoes, sexual transmission also contributes to the virus outbreak. The epidemiological patterns of these viruses suggest that Zika virus could cause other outbreaks, particularly in tropical regions with high vector concentration. To plan and prepare for a counter-control measure, it is important to study the previous cases. Hence, the control model is proposed from the deterministic model of Zika virus infection. Regarding control measures, the control functions for these strategies; vector elimination, vector-to-human contact reduction, and human-to-human contact reduction are introduced into the system. The necessary conditions for the optimal controls are determined using Pontryagin's maximum principle and the optimality system is solved using Rung-Kutta fourth order scheme. Consequently, numerical results of the system with control and the system without control are shown and discussed.

Modeling the Impact of Optimal Control Strategies on the Dynamics of Zika Virus Disease Using the Sterile Insect Technology

“…The Pontryagin's maximum principle given in [25] by L.S Pontryagin's in 1956 as a vital result in optimal control was used in this work, the theory that provides a necessary but not sufficient condition that must be satisfied by the optimal solution to optimal control problem, [19]. The Pontryagin maximum principle majorly converts a constrained control problem to unconstrained one by introducing an additional variable to the original problem, [19]. The Pontryagin minimum principle given below, gives the condition under which ) , ( * * u x is optimal.…”

“…Optimal control is a vital mathematical method deciding a strategy regarding epidemic control with provided scenarios, [15,16,17,18]. Chaikham N et al [19] presented a model on the optimal control of zika infection; they used the Pontryagin's maximum principle to determine the necessary conditions for the optimal control. Their result shows that optimal control helps in decreasing the number of individuals infected and at the long run the spread of the disease.…”

“…There is a possibility that zika virus outbreak may emerge again in the future, especially in the high vector concentrations areas [24], to this end, we present in this work an environmental pleasant control method called the Sterile Insect Technology (SIT) to study the transmission dynamics of zika virus infection where we extended the work of [8] to formulate a mathematical model of zika virus infection using the Sterile Insect Technology with human population incorporated. We also incorporated Optimal Control measures following the method used by [19]. The Sterile Insect Technology is a kind of control for insects like mosquitoes that does not have any harmful effect on the environment.…”

Sub-Optimal Control in the Zika Virus Epidemic Model Using Differential Evolution

“…In this paper, we develop the ZIKV virus infection model using some previous works [12,13,18]. The model consists of three populations: adult humans, newborn babies human, and mosquitoes.…”

“…The indirect approaches, such as Pontryagin's Maximum Principle [21] and shooting method, are popular to find optimal solutions of some flavivirus control problems, for example, chikungunya [16] and dengue [17]. Previously, the authors also studied the optimal control problem of the Zika virus infection [18] by the indirect approach. However, the implementations for health authorities by these studies [16,17] are difficult to practically apply since the policies have to be varied continuously.…”