Volume 1, Issue 2, December 2017, pp 49-60
G. Devipriya
Department of Mathematics, Stella Maris College, Chennai - 600 086, India
A mathematical model of Dengue virus transmission consist of human and mosquito compartments by incorporating a control strategy of imperfect treatment and delay in vector maturation is considered. Analytical solution of the model is obtained with aid of Homotopy Perturbation Method. Numerical solutions are obtained and the results are discussed graphically.
Epidemic Models, Delayed Dengue model, Homotopy Perturbation Method, Numerical Simulations.
1. Abdullah Idris Enagi, Musa Bawa, Abdullah Muhammad Sani, Mathematical Study of Diabetes and its Complication Using the Homotopy Perturbation Method, Int. J. Math. Comput. Sci. 2017; 12: 43 - 63.
2. Abubakar, S., N.I. Akinwande, O.R. Jimoh, F.A. Oguntolu, and O.D. Ogwumu, Approximate Solution of SIR Infectious Disease Model Using Homotopy Perturbation Method (HPM), Pacific J. Sci. Tech., 2013; 14: 163-169.
3. Bonyah Ebenezer,, Asfandiyar Khan, Muhammad Altaf Khan, Saeed Islam, Analytical Solution of the Ebola Epidemic Model by Homotopy Perturbation Method, J. Appl. Environ. Biol. Sci., 2016; 6: 41-49.
4. Guihong Fan, Junli Liu, P. van den Driessche, Jianhong Wu and Huaiping Zhu, The impact of maturation delay of mosquitoes on the transmission of West Nile virus, Math. Biosci., 2010: 228: 119 - 126.
5. J.H. He, Homotopy perturbation method: A new nonlinear analytical technique, Appl. Math.Comput., 2003; 135: 73 - 79.
6. Helena Sofia Rodrigues, M. Teresa T. Monteiro and Delfim F. M. Torres, Seasonality effects on Dengue: basic reproduction number, sensitivity analysis and optimal control, Math. Meth. Appl. Sci., 2014; DOI: 10.1002/mma.3319.
7. Lin-Fei Nie and Ya-Nan Xue, The roles of maturation delay and vaccination on the spread of Dengue virus and optimal control, Adv. Difference Equ., 2017; DOI: 10.1186/s13662-017-1323-y.
8. Muhammad Altaf Khan, Islam S., Murad Ullah, Sher Afzal Khan, Zaman G. and Syed Farasat Saddiq, Analytical Solution of the Leptospirosis Epidemic model by Homotopy Perturbation method,Res.J.Recent Sci., 2013; 2: 66 - 71.
9. Islam S., Syed Farasat Saddiq, Zaman G., Muhammad Altaf Khan, Sher Afzal Khan, Farooq Ahmad and Murad Ullah, Analytical Solution of the SEIV Epidemic model by Homotopy Perturbation method, VFAST Transactions on Mathematics, 2013; 1: 1 - 7.