SVIR Epidemic Model with Non Constant Population

Joko Harianto, Titik Suparwati


In this article, we present an SVIR epidemic model with deadly deseases and non constant population. We only discuss the local stability analysis of the model. Initially the basic formulation of the model is presented. Two equilibrium point exists for the system; disease free and endemic equilibrium point. The local stability of the disease free and endemic equilibrium exists when the basic reproduction number less or greater than unity, respectively. If the value of R0 less than one then the desease free equilibrium point is locally asymptotically stable, and if its exceeds, the endemic equilibrium point is locally asymptotically stable. The numerical results are presented for illustration.



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Diekmann,O., and Heesterbeek,J.A.P., Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis, and Interpretation, John Wiley and Sons, Chichester, 2000.

Driessche, P.V.D., Watmough, J., "Reproduction Number and Sub-threshod Endemic Equilibria for Compartmental Models of Disease Transmission," Mathematical Biosciences 180, pp. 29-48, 2002.

H.W. Hethcote, J.W.V. Ark, Epidemiological models for heterogeneous populations: proportionate mixing, parameter estimation, and immunization programs, Math. Biosci. 84 (1987) 85

Kermack, W. O. and McKendrick, A. G., "A Contribution to the Mathematical Theory of Epidemics,"Proc. Roy. Soc. Lond., A 115, pp. 700-721, 1927.

Khan, Muhammad Altaf, Saeed Islam and others, "Stability Analysis of an SVIR Epidemic Model with Non-linear Saturated Incidence Rate," Applied Mathematical Sciences, vol. 9, no. 23, .1145-1158, 2015.

Kribs-Zaleta, C., Velasco-Hernandez, J., "A Simple Vaccination Model with Multiple Endemic State," Mathematical Biosciences, vol. 164, pp. 183-201, 2000.

Lancaster, P.,"Theory of Matrices", Academic Press, New York, 1969.

Liu, Xianing, and others, "SVIR Epidemic Models with Vaccination Strategies," Journal of Theoretical Biology 253, 1-11, 2007.

Zaman, G., and others, "Stability Analysis and Optimal Vaccination of an SIR Epidemic Model," Bio Systems 93, pp. 240-249, 2008. biosystems.2008.05.004



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