Mathematical modelling and optimal control of dengue transmission with saturated treatment function and asymptomatic immigration

Abstract

Dengue fever is a mosquito-borne disease that has been declared as one of the major public health problems in many tropical climate countries. Rising dengue dissemination could be caused by population growth and urbanisation, long-distance travel, lack of sanitation, and ineffective mosquito population control. In light of this issue, this study introduces deterministic models for optimal control problems pertaining to dengue transmission. The first new model incorporates nonlinear incidence and treatment function since disease occurrences are inherently nonlinear and treatment might be delayed as public health resources are sometimes limited. Although nonlinear incidence functions in dengue transmission models have been proposed in previous studies, the use of both nonlinear incidence and treatment functions are limited. Another model based on a compartment of asymptomatically infected humans with the appearance of constant immigration into the compartment is also introduced. This is in accordance with the fact stated by the World Health Organization, that the majority of dengue disease cases are asymptomatic. Several dengue transmission models with asymptomatic compartment can also be found in the literature, but none have assumed the existence of constant immigration for this compartment model. Subsequently, a threshold governing disease persistence within a population is determined and the existence of endemic equilibrium is identified. Then, the analysis of the stability of equilibria and numerical simulations are presented accordingly. Also, the optimal control problems are formulated based on the two new deterministic models in which time-dependent control and prevention measures are used. Then, the optimal control parameters are identified, and the corresponding optimality systems are set up. Based on the formed optimality system, numerical simulation is carried out. The results of numerical simulation can be used as a guideline in implementing prevention and control measures for dengue transmission. The results also revealed that self-protection strategy, such as using mosquito repellents and wearing protective clothes, is an important preventive measure in combating dengue transmission.