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

Authors

  • Melyssa Mentari Tjioenata Universitas Pelita Harapan
  • Samuel Lukas Universitas Pelita Harapan
  • Dina Stefani Universitas Pelita Harapan
  • Petrus Widjaja Universitas Pelita Harapan

DOI:

https://doi.org/10.19166/isd.v8i1.566

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.

References

<p>Kementerian Kesehatan Republik Indonesia. Infodatinsituasi-demam berdarah-dengue, 2018. Available at http://www.depkes.go.id/resources/d ownload/pusdatin/info datin/InfoDatin-Situasi-DemamBerdarah-Dengue. [Diakses pada 22 September 2019].</p><p>World Health Organization. Fact sheet dengue and severe dengue, 2019. Available at https://www.who.int/newsroom/factsheets/detail/dengue-and-severedengue. [Diakses pada 22 September 2019].</p><p>Melanie Mitchell. An introduction to genetic algorithms. MIT press, 1998.</p><p>Matt J Keeling and Pejman Rohani. Modeling infectious diseases in humans and animals. Princeton University Press, 2011.</p><p>Erwin Kreyszig, Herbert Kreyszig, and E. J. Norminton. Advanced Engineering Mathematics. Wiley, Hoboken, NJ, tenth edition, 2011</p>

Published

2023-02-17