Solution of a Vaccination Based SIR Epidemic Model by Homotopy Analysis Method
Abstract
Modeling infectious diseases helped out to understand and overcome epidemics. This paper isbased on epidemic model SIR, which fits well tomany epidemiological diseases. Basic idea ofHomotopy Analysis Method (HAM)is discussed and employed to compute an approximation to thesolution of nonlinear system of differential equations. The effect of vaccination on the dynamics ofchildhood disease described by SIR model is monitored using HAM. The qualitative analysis revealsthe vaccination reproduction number for disease control and eradication. MATLAB is used to carryout the computations. Graphical results are presented and discussed quantitatively.References
Rekha Mehra, Pawan Kumar Inaniya “Design of Photonic Crystal Fiber for Ultra Low Dispersion in Wide Wavelength Range with Three Zero Dispersion Wavelengths” Citation: AIP Conf. Proc. 1324, 175 (2010).
Karen Marie Hilligsoe,“Wave Propagation in Photonic Crystal Fibers”. PhD Dissertation Department of Physics and Astronomy and Department of Chemistry, University of Aarhus 2005.
Razzak. S.M.A, Namihira Y, Begum F,“Ultra flattened dispersion Photonic crystal fiber”, Electronics Letters 43 (11), pp. 615- 617, 2007.
Saeed Olyaee and Fahimeh Taghipour “A new design of photonic crystal fiber with ultraflattened dispersion to simultaneously minimize the dispersion and confinement loss”Journal of Physics: Conference Series 276 (2011) 012080
Vineet Agrawal, Ravindra Kumar Sharma, Ashish Mittal “Designing the Properties of Zero Dispersion Photonic Crystal Fiber with Concentric Missing Ring”IJECT Vo l. 4, 2013.
Rekha Mehra , Pawan Kumar Inaniya “Design of Photonic Crystal Fiber for Ultra Low Dispersion in Wide Wavelength Range with Three Zero Dispersion Wavelengths” Citation: AIP Conf. Proc. 1324, 175 (2010)
Hansen K P 2003 “Dispersion flattened hybridcore nonlinear photonic crystal fiber”Opt. Express 11, 1503
Hai N H, Namihiray Y, Kaijage S F, Kinjo T, Begum F, Razzak S M A, and Zou N 2008“Multiple defect-core hexagonal photonic crystal fiber with flattened dispersion an polarization maintaining properties” Opt. Review 15, 31
J. C. Knight, T. A. Briks, P. S. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett., vol. 21, no. 19, pp. 1547–1549, 1996.. D. Ferrarini, L. Vincetti, and M. Zoboli, “Leakage properties of photonic crystal fibers,” Opt. Express, vol. 10, no. 23, pp. 1314–319, (2002).
A. Ferrando, E. Silvestre, and P. Andr´es, “Designing the properties of dispersion-flattened photonic crystal fiber,” Opt. Express, vol. 9, no. 13, pp. 687–697, 2001.
L. P. Shen, W. P. Huang, and S. S. Jian, “Design of photonic crystal fibers for dispersion- related applications,” J. Lightwave Technol., vol. 21, no. 7, pp. 1644–1651, 2003
N. Guan, S. Habu, K. Takenaga, K. Himeno, and A. Wada, “Boundary element method for analysis of holey optical fibers,” J. Lightwave Technol., vol. 21, no. 8, pp. 1787–1792, 2003.
