MATHEMATICAL MODEL OF DENGUE CONTROL WITH CONTROL OF MOSQUITO LARVAE AND MOSQUITO AFFECTED BY CLIMATE CHANGE
Consider a SIR model for the spread of dengue hemorrhagic fever involving three populations, mosquito eggs, mosquitoes, and humans. The parameters of the SIR model were estimated using rainfall data and air temperature for the cities of Pekanbaru and Solok. The main aim of this paper is to determine the effect of mosquito larvae and adult mosquito control on the spread of the dengue virus. Numerical solutions were also presented by using the Runge-Kutta method of order 4. Based on the results, the SIR model was obtained by involving the control parameters of mosquito larvae and adult mosquitoes. Besides, the mosquito population is affected by changes in temperature, rainfall, and fog. Numerical simulations illustrate that the number of infected mosquitoes and infected humans is influenced by the parameters of the percentage of mortality of mosquito larvae and adult mosquitoes.
Kemenkes, â€œDemam Berdarah Dengue,â€ Buletin Jendela Epidemiologi, vol. 2, p. 48, 2010.
M. M. Rossi, L. F. Lopez, and E. Massad, â€œThe Dynamics of Temperature- And Rainfall-Dependent Dengue Transmission in Tropical Regions,â€ Annals of Biometrics & Biostatistics, vol. 2, no. 2, pp. 1â€“6, 2015.
A. Sumi, E. F. O. Telan, H. Chagan-Yasutan, M. B. Piolo, T. Hattori, and N. Kobayashi, â€œEffect of temperature, relative humidity and rainfall on dengue fever and leptospirosis infections in Manila, the Philippines,â€ Epidemiology and Infection, vol. 145, no. 1, pp. 78â€“86, 2017, doi: 10.1017/S095026881600203X.
A. K. Supriatna and E. Soewono, â€œModel Matematika Penyebaran Penyakit Demam Berdarah,â€ Jurnal Bionatura, vol. 2, no. 3, pp. 1â€“13, 2000.
S. Side and S. M. Noorani, â€œA SIR model for spread of dengue fever disease (simulation for South Sulawesi, Indonesia and Selangor, Malaysia),â€ World Journal of Modelling and Simulation, vol. 9, no. 2, pp. 96â€“105, 2013.
S. C. Chen and M. H. Hsieh, â€œModeling the transmission dynamics of dengue fever: Implications of temperature effects,â€ Science of the Total Environment, vol. 431, pp. 385â€“391, 2012, doi: 10.1016/j.scitotenv.2012.05.012.
G. R. Phaijoo and D. B. Gurung, â€œModeling Impact of Temperature and Human Movement on the Persistence of Dengue Disease,â€ Computational and Mathematical Methods in Medicine, vol. 2017, 2017, doi: 10.1155/2017/1747134.
R. Taghikhani and A. B. Gumel, â€œMathematics of dengue transmission dynamics: Roles of vector vertical transmission and temperature fluctuations,â€ Infectious Disease Modelling, vol. 3, pp. 266â€“292, 2018, doi: 10.1016/j.idm.2018.09.003.
P. S. Murdoch, J. S. Baron, and T. L. Miller, â€œPotential Effects of Climate Change on Surface â€ Water,â€ vol. 36, no. 2, p. 2018, 2018.
P. Chanprasopchai, P. Pongsumpun, and I. M. Tang, â€œEffect of Rainfall for the Dynamical Transmission Model of the Dengue Disease in Thailand,â€ Computational and Mathematical Methods in Medicine, vol. 2017, 2017, doi: 10.1155/2017/2541862.
A. Bustamam, D. Aldila, and A. Yuwanda, â€œUnderstanding Dengue Control for Short- and Long-Term Intervention with a Mathematical Model Approach,â€ Journal of Applied Mathematics, vol. 2018, 2018, doi: 10.1155/2018/9674138.
Y. H. Cheng et al., â€œAssessing health burden risk and control effect on dengue fever infection in the southern region of Taiwan,â€ Infection and Drug Resistance, vol. 11, pp. 1423â€“1435, 2018, doi: 10.2147/IDR.S169820.
K. Chudej and A. Fischer, â€œOptimal Vaccination Strategies for a new Dengue Model with two Serotypes,â€ IFAC-PapersOnLine, vol. 51, no. 2, pp. 13â€“18, 2018, doi: 10.1016/j.ifacol.2018.03.003.
L. F. Nie and Y. N. Xue, â€œThe roles of maturation delay and vaccination on the spread of Dengue virus and optimal control,â€ Advances in Difference Equations, vol. 2017, no. 1, 2017, doi: 10.1186/s13662-017-1323-y.
C. Schreppel and K. Chudej, â€œNumerical optimal control applied to an epidemiological model,â€ IFAC-Papers On Line, vol. 51, no. 2, pp. 1â€“6, 2018, doi: 10.1016/j.ifacol.2018.03.001.
Copyright (c) 2021 Wartono Wartono, Mohammad Soleh, Yuslenita Muda
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.