Application of MADM in Identifying the Transmission Rate of Dengue fever: A Case Study of Shah Alam, Malaysia
Identifying parameters in an epidemic model is one
of the important aspect of modeling. In this paper, we suggest a
method to identify the transmission rate by using the multistage
Adomian decomposition method. As a case study, we use the data of
the reported dengue fever cases in the city of Shah Alam, Malaysia.
The result obtained fairly represents the actual situation. However, in
the SIR model, this method serves as an alternative in parameter
identification and enables us to make necessary analysis for a smaller
interval.
[1] Ministry of Health, Malaysia. (2011, January 06). Dengue Fever and
Chikugunya situation in Malaysia. Retrieved January 25, 2011, from
Ministry of Health, Malaysia: http://www.moh.gov.my/press_release/96
[2] H. Hethcote, "The Mathematics of Infectious Diseases," SIAM Review,
vol. 42, no. 4, pp. 599-653, 2000.
[3] L. Esteva and C. Vargas, "Coexistence of different serotypes of dengue
virus," Journal of Mathematical Biology , vol. 46, pp. 31-47, 2003.
[4] M. Derouich, A. Boutayeb, and E. Twizell, " A model of dengue
fever," BioMedical Engineering OnLine, vol. 2:4, pp. 1-10, Feb. 2003.
[5] G. Gonzalez-Parra, A. J. Arenas, and L. Jodar, " Piecewise Finite Series
Solutions of Seasonal Disease Models using Multistage Adomian
Method," Communications in Nonlinear Science and Numerical
Simulation , vol. 14, pp. 3967-3977, 2009.
[6] M. Chowdhury, I. Hashim, and S. Mawa, " Solution of prey-predator
problem by numeric-analytic technique," Nonlinear Science and
Numerical Simulation , vol. 14, pp. 1008-1012, 2009.
[7] I. Hashim, M. Noorani, R. Ahmad, S. Bakar, E. Ismail, and A. Zakaria,
"Accuracy of the Adomian decomposition method applied to the Lorenz
system," Chaos, Soliton and Fractals , vol. 28, pp. 1149-1159, 2006.
[8] S. Manseur, N. Messaoudi, and Y. Cherrualt, " Parameter identification
of an HIV model by the combined Adomian/Alienor method,"
Kybernetes , vol. 35 (10), pp. 1725-1734, 2006.
[9] G. Adomian, Solving frontier problems of physics: The decomposition
method. Boston: Kluwer Academic Publishers, 1994.
[10] A. M. Wazwaz, " A new algorithm for calculating Adomian
polynomials for nonlinear operators," Applied Mathematics and
Computation , vol. 111, pp. 53-69, 2000.
[11] J. Biazar, " Solution of the epidemic model by Adomian decomposition
method," Applied Mathematics and Computation , vol. 173, pp.1101-
1106, 2006.
[12] M. A. El-Tawil, A. A. Bahnasawi, and A. Abdel-Naby, " Solving Riccati
differential equation using Adomian's decomposition method," Applied
Mathematics and Computation , vol. 157, pp. 503-514, 2004.N. Yusoff,
H. Budin, ans S. Ismail, "Parameter estimation of the SIR model using
the multistage Adomian decomposition method (MADM)" in
Proceedings of the 6th IMT-GT International Conference on
Mathematics, Statistics and its Applications (ICMSA 2010), 2010,
pp.635-645
[13] M. Burattini, M. Chen, A. Chow, F. Coutinho, K. Goh, Lopez, et al.,
"Modelling the control strategies against dengue in Singapore,"
Epidemiology and Infection , vol. 136, pp. 309-319, 2008.
[1] Ministry of Health, Malaysia. (2011, January 06). Dengue Fever and
Chikugunya situation in Malaysia. Retrieved January 25, 2011, from
Ministry of Health, Malaysia: http://www.moh.gov.my/press_release/96
[2] H. Hethcote, "The Mathematics of Infectious Diseases," SIAM Review,
vol. 42, no. 4, pp. 599-653, 2000.
[3] L. Esteva and C. Vargas, "Coexistence of different serotypes of dengue
virus," Journal of Mathematical Biology , vol. 46, pp. 31-47, 2003.
[4] M. Derouich, A. Boutayeb, and E. Twizell, " A model of dengue
fever," BioMedical Engineering OnLine, vol. 2:4, pp. 1-10, Feb. 2003.
[5] G. Gonzalez-Parra, A. J. Arenas, and L. Jodar, " Piecewise Finite Series
Solutions of Seasonal Disease Models using Multistage Adomian
Method," Communications in Nonlinear Science and Numerical
Simulation , vol. 14, pp. 3967-3977, 2009.
[6] M. Chowdhury, I. Hashim, and S. Mawa, " Solution of prey-predator
problem by numeric-analytic technique," Nonlinear Science and
Numerical Simulation , vol. 14, pp. 1008-1012, 2009.
[7] I. Hashim, M. Noorani, R. Ahmad, S. Bakar, E. Ismail, and A. Zakaria,
"Accuracy of the Adomian decomposition method applied to the Lorenz
system," Chaos, Soliton and Fractals , vol. 28, pp. 1149-1159, 2006.
[8] S. Manseur, N. Messaoudi, and Y. Cherrualt, " Parameter identification
of an HIV model by the combined Adomian/Alienor method,"
Kybernetes , vol. 35 (10), pp. 1725-1734, 2006.
[9] G. Adomian, Solving frontier problems of physics: The decomposition
method. Boston: Kluwer Academic Publishers, 1994.
[10] A. M. Wazwaz, " A new algorithm for calculating Adomian
polynomials for nonlinear operators," Applied Mathematics and
Computation , vol. 111, pp. 53-69, 2000.
[11] J. Biazar, " Solution of the epidemic model by Adomian decomposition
method," Applied Mathematics and Computation , vol. 173, pp.1101-
1106, 2006.
[12] M. A. El-Tawil, A. A. Bahnasawi, and A. Abdel-Naby, " Solving Riccati
differential equation using Adomian's decomposition method," Applied
Mathematics and Computation , vol. 157, pp. 503-514, 2004.N. Yusoff,
H. Budin, ans S. Ismail, "Parameter estimation of the SIR model using
the multistage Adomian decomposition method (MADM)" in
Proceedings of the 6th IMT-GT International Conference on
Mathematics, Statistics and its Applications (ICMSA 2010), 2010,
pp.635-645
[13] M. Burattini, M. Chen, A. Chow, F. Coutinho, K. Goh, Lopez, et al.,
"Modelling the control strategies against dengue in Singapore,"
Epidemiology and Infection , vol. 136, pp. 309-319, 2008.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:62076", author = "Nuraini Yusoff and Harun Budin and Salemah Ismail", title = "Application of MADM in Identifying the Transmission Rate of Dengue fever: A Case Study of Shah Alam, Malaysia", abstract = "Identifying parameters in an epidemic model is one
of the important aspect of modeling. In this paper, we suggest a
method to identify the transmission rate by using the multistage
Adomian decomposition method. As a case study, we use the data of
the reported dengue fever cases in the city of Shah Alam, Malaysia.
The result obtained fairly represents the actual situation. However, in
the SIR model, this method serves as an alternative in parameter
identification and enables us to make necessary analysis for a smaller
interval.", keywords = "dengue fever, multistage Adomian decomposition
method, Shah Alam, SIR model", volume = "5", number = "5", pages = "779-6", }
