Local Stability Analysis of an SVIR Epidemic Model

Joko Harianto

Abstract


In this paper, we present an SVIR epidemic model with deadly deseases. Initially the basic formulation of the model is presented. Two equilibrium point exists for the system; disease free and endemic equilibrium. 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 is locally stable, and if its exceeds, the endemic equilibrium is locally stable. The numerical results are presented for illustration.

Keywords


Applied Mathematics

Full Text:

PDF

References


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.

http://dx.doi.org/10.1016/s0025-5564(02)00108-6

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.

http://dx.doi.org/10.1098/rspa.1927.0118

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.

http://dx.doi.org/10.12988/ams.2015.41164

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

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

http://dx.doi.org/10.1016/j.jtbi.2007.10.014

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

http://dx.doi.org/10.1016/j. biosystems.2008.05.004




DOI: http://dx.doi.org/10.18860/ca.v5i1.4388

Refbacks

  • There are currently no refbacks.

Comments on this article

View all comments


Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Editorial Office
Mathematics Department,
Universitas Islam Negeri Maulana Malik Ibrahim Malang
Jalan Gajayana 50 Malang, Jawa Timur, Indonesia 65144
Phone (+62) 81336397956, Faximile (+62) 341 558933
e-mail: cauchy@uin-malang.ac.id / jo_alkanderi57@yahoo.co.id
 

Creative Commons License
Cauchy (ISSN: 2086-0382 / E-ISSN: 2477-3344) by http://ejournal.uin-malang.ac.id/index.php/Math is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.