Modelling of Dengue Virus Transmission with Optimal Control

Abstract

An infected female mosquito bite is how the virus that causes dengue fever is
spread to humans. In this research, a mathematical model that includes vector control
and human susceptibility awareness is suggested to describe the transmission of the
two strains of Dengue virus between humans and mosquitoes. This study aims to
establish and analyze a mathematical model of dengue fever with the application of
optimal control. The results of this study are expected to be able to provide information
to the government, as well as material for further research. The method used to solve
the above problem is to use the Pontryagin maximum principle method, which is then
solved by the fourth-order runge kutta numerical method. The simulations carried out
showed that the population of susceptible and infected human individuals decreased
with optimal control, while the population of recovered individuals increased after
optimal control was given. In the mosquito population, after being given optimal
control, the mosquitoes capable of being infected (susceptible) and the mosquitoes
infected with the dengue virus (infected) decreased compared to before the optimal
control was given. This shows that the optimal control works well on the mathematical
model of dengue fever. Theoretical results and numerical simulations indicate that
measures to increase awareness of the self-protection of infected and susceptible
humans should be taken and mosquito control measures are needed to prevent
transmission of Dengue virus from mosquitoes to humans.