Asymptomatic carriers in transmission dynamics of dengue with control interventions

In this paper, we introduce a dengue disease transmission model with symptomatic and asymptomatic infectious classes. We obtain the threshold dynamics governed by the basic reproduction number of the system. We obtain sensitivity analysis of threshold dynamics to recognize the dominant factors that seriously affect the dengue infection. It has been shown that the biting rate and the rate of asymptomatic cases are more sensitive to the basic reproduction number, and predicts that control of mosquito size plays an essential role in reducing equilibrium level of dengue infection. Hence, the use of mosquito nets and control of population size of mosquitoes are highly suggested to the public. We use optimal control theory to help the public health personnel and biologists to adopt better understanding of the modeling strategies to control dengue fever. We apply preventive control, treatment, and insecticide spray to reach the desire objectives; moreover, the existence of the proposed optimal control problem is established analytically and achieves necessary conditions for optimal controls. The simulations obtained suggested that control measures such as mosquito eradication and preventive strategies effectively eradicate and control dengue infections during the epidemic.