Application of Mosquito Net Control in a New Dynamics of Dengue

Nilwan Andiraja (UIN Sultan Syarif Kasim Riau)

Justek : Jurnal Sains Dan Teknologi
Vol 9, No 2 (2026): June

This study discusses the application of mosquito net control in the SIR-UV model for the spread of dengue fever. The study has a specific objective to analyze the effectiveness of mosquito net control on the vulnerable human population to reduce the number of people infected with dengue fever. This research begins by forming a new SIR-UV mathematical model (state equation) with mosquito net control in the class of vulnerable human population and creating a new objective function to minimize the population of humans infected with dengue fever. Next, using Pontryagin's principle, the Hamiltonian function was formed. From the Hamiltonian function, the costate equation and the optimal control for the use of mosquito nets were obtained. The next step is to change the state equation and the costate equation using the 4th order Runge-Kutta method. Then a numerical simulation is performed, with the forward sweep method determining the solution to the state equation, and the backward sweep method for solving the costate equation. Numerical simulations will be conducted to observe the effects of control on the class of human population infected. The numerical simulations will use some data from previous research so that the simulation results can be compared with the previous research findings. The simulation results show that the use of mosquito nets on the vulnerable human population class can reduce the population of humans infected with dengue fever, where from the initial time of day 0, the graph of infected humans immediately drops below 20 days and continues to approach zero until day 100. It has same results for mosquitoes infected, which decreased immediately from the start continued to approach zero until days 100. In contrast, without control, there is a spike in the number of infected humans at the beginning and will approach zero by day 80 and it took until day 60 for the mosquitoes infected population with dengue virus to approach 0. Therefore, the use of mosquito nets on the vulnerable human population can reduce the number of humans infected with dengue fever and, of course, contribute to minimizing the spread of dengue fever.