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# Analytical Solution of the Leptospirosis Epidemic model by Homotopy Perturbation method

Author Affiliations

• 1Department of Mathematics, Abdul Wali Khan University Mardan, PAKISTAN
• 2 Department of Mathematics, Islamia College University, Peshawar, PAKISTAN
• 3 Department of Computer Science, Abdul Wali Khan University Mardan, PAKISTAN
• 4 Department of Mathematics, University of Malakand Chakdara, Dir (lower), PAKISTAN

Res. J. Recent Sci., Volume 2, Issue (8), Pages 66-71, August,2 (2013)

## Abstract

In this paper, we consider a mathematical model of leptospirosis disease consisting of differential equations. We apply the Homotopy perturbation method to the proposed model to find both the analytic and approximate solutions. From our solutions, we obtained that Homotopy perturbation method is one of the most important method, like just few perturbation terms are sufficient for obtaining a reasonable accurate solution. The solution obtain from this method is good as compared to other standard numerical methods.

## References

1. Zaman G., Khan M.A., Islam S. et al., Modeling Dynamical Interactions between LeptospirosisInfected Vector and Human Population, Appl.Math. Sci, 6(26), 1287–1302 (2012)
2. Chitnis N., Smith T. and Steketee R., A mathematical model for the dynamics of malaria inmosquitoes feeding on a heterogeneous host population, J. Biol. Dyn., , 259-285 (2008)
3. M. Derouich and A. Boutayeb, Mathematical modelling and computer simulations of Dengue fever, App. Math.Comput.,177, 528-544 (2006)
4. Esteva L. and Vergas C., A model for dengue disease with variable human populations, J. Math. Biol., 38, 220-240 (1999)
5. Pongsuumpun P., Miami T. and Kongnuy R., Age structural transmission model for leptospirosis, The third International symposium on Biomedical engineering, 411-416 (2008)
6. Triampo W., Baowan D., Tang I.M., Nuttavut N., WongEkkabut J. and Doungchawee G., Asimple deterministic model for the spread of leptospirosis in Thailand, Int. J. Bio. Med. Sci., , 22-26 (2007)
7. Zaman G., Dynamical behavior of leptospirosis disease and role of optimal control theory, Int. J. Math. Comp., 7, 10 (2010)
8. He J.H., Variational iteration method: A kind of nonlinear analytical technique: Some examples, Int. J. Non-Linear Mech., 34(4), 699-708 (1999)
9. He J.H., Homotopy perturbation method for solving boundary value problems, Phys. Letter.A., 350, 87-88 (2006)
10. He J.H., Recent development of the homotopy perturbation method, Topological methods in nonlinear analysis, 31(2), 205-209 (2008)
11. He J.H., An elementary introduction to the homotopy perturbation method, Comput. Maths.App., 57(3), 410-412 (2009)
12. He J.H., An elementary introduction to recently developed asymptotic methods and nanomechanics in textile engineering, Int. J. Mod. Phys. B, 22(21), 3487-3578 (2006)
13. Ali J., Islam S., Islam S.U. and Zaman G., The solution of multipoint boundary value problems by the Optimal Homotopy Asymptotic Method, Comput.Math. Appl., 59,2000-2006 (2010)
14. Saddiq S.F., Khan M.A., Khan S.A., Ahmad F. and Ullah M., Analytical solution of an SEIV epidemic model by Homotopy Perturbation method, VFAST Transactions on Mathematics, 1(2),(2013)
15. Khan M.A., Islam S., Ullah M., Khan S.A., Zaman G., Arif M. and Sadiq S.F., Application of Homotopy Perturbation Method to Vector Host Epidemic Model with Non-Linear Incidences, Research Journal of Recent Sciences, 2(6), 90-95 (2013)
16. Ullah R., Zaman G. and Islam S., Stability analysis of a general SIR epidemic model. VFAST Transactions on Mathematics, 1(1), 16–20 (2013)
17. Saddiq S.F., Khan M.A., Khan S.A., Ahmad F. and Ullah M., Analytical solution of an SEIV epidemic model by Homotopy Perturbation method, VFAST Transactions on Mathematics, 1(2), 1-7 (2013)