Analysis Of The Sirs Model Of The Spread Of Dengue Hemorrhagic Fever Using Runge-Kutta Method And Genetic Algorithm

Abstract

Dengue Hemorrhagic Fever is a contagious disease that often occurs in Indonesia. Dengue Hemorrhagic Fever, caused by the Dengue Virus, has four serotypes : DEN-1, DEN-2, DEN-3 and DEN-4. Someone can be infected four times, once for each serotype. After recovering from one serotype, a person gets a lifetime of immunity against that serotype. In this paper a model will be created for modeling the spread of Dengue Hemorrhagic Fever with assumption there are only two serotypes, namely DEN-1 and DEN-2. Model formed based on SIR Model (Susceptible, Infected, Recovered) and SIRS Model (Susceptible, Infected, Recovered, Susceptible). The changes in populations over time are written into a system of differential equations. The system of differential equations is then used to do an equilibrium point analysis. The numerical solution for the system of differential equations can be found using the Runge-Kutta Method. Genetic Algorithm are used to find the values of parameters in the model that are unknown. A series of simulations are performed to get the combination that produces the Genetic Algorithm system that will produce the best approximation solution. The combination includes population size, selection value, crossover value and mutation value. This best combination then will produce an approximation solution with the smallest error.