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

Nonthamon Chaikham and Wannika Sawangtong

 

In this work, we develop the ZIKV virus infection model consisting of three populations: adult humans, newborn baby human, and mosquitoes. Three controls are selected from the suggestions of the World Health Organization (WHO) and health authorities: using larvicide and adulticide to reduce the mosquito population, using insect repellents to prevent mosquito biting, and abstaining from sexual activity or using protection to prevent pregnancy. We proposed sub-optimal control problem with three control parameters: vector elimination, human–vector reduction, and human–human contact reduction. To find the control solution which is easy to implement, we partitioned the controls into discrete intervals. By using Differential Evolution, we solved and presented the numerical scenarios with four-time horizons and eight-time horizons. The simulations of both controls efficiently reduce the number of exposed and infected patients where the model with eight intervals yields a slightly better result. Controls u1, using repellents to prevent mosquito biting, and u2, avoiding pregnancy and unsafe sexual activity, should be applied mostly during the peak of the disease. After the disease dies out or becomes stable, the level of both controls will decrease. Mosquito elimination should be the first focus in controlling the disease, corresponding to the primary procedure announced by general health authorities. However, the cost associated with each control in this simulation is set to be equal. The consideration of adjusting the relative cost according to alternative scenarios might provide different results. Additionally, if more information is available in the future, the simulations should be conducted again using more precise data.