MATHEMATICAL MODELS AND STRATEGIES TO CONTROL THE SPREAD OF DENGUE HEMORRHAGIC FEVER WITH VACCINATION - Janice Wijaya, Gracia
Dengue hemorrhagic fever is an infectious disease caused by the transmission of the Dengue virus and transmitted through the Aedes aegypti mosquito to humans. Indonesia is one of the countries with the most cases of dengue fever in Southeast Asia. Therefore, the spread of dengue fever must be controlled to reduce the increase in cases. The control strategy reviewed in this final assignment is education on prevention of Dengue Hemorrhagic Fever and vaccination. This research constructs a mathematical model of the spread of Dengue Hemorrhagic Fever by reviewing the effect of vaccination using a modified SIR compartment model involving mosquito and human populations. Vaccination is used by susceptible humans. Numerical simulations were carried out to analyze the behavior of each compartment in the spread of Dengue Hemorrhagic Fever. Through numerical results, it is known that the factors that influence the spread of Dengue Hemorrhagic Fever are the rate of transmission of the Dengue virus from mosquitoes to humans, the rate of recovery from the disease, the rate of vaccination, and the rate of loss of immunity to the Dengue virus. Model analysis is carried out by determining the equilibrium point, existence and stability. To suppress the spread of disease, optimal control methods are also carried out with three control strategies, namely, there is a chance of success for individuals who have been exposed to counseling to carry out preventive measures, there is regulation of the proportion of vaccinations given to vulnerable individuals, and there is a chance of success for individuals who have been affected. counseling to carry out preventive measures and the proportion of vaccinations given to vulnerable individuals. This optimal control aims to minimize infected individuals with minimal costs. The results of the numerical simulation of the optimal control problem show that the combination strategy of regulating individuals who have been exposed to counseling to carry out preventive measures and the proportion of vaccinations given to susceptible individuals is the most effective strategy to reduce infected individuals by 0.6% at a cost of 146,2197.