Abstract
In this paper, we consider an SIRS model with non linear incidence and disease induced death rate in which we consider the incidence rate KIpSq for p = 2 and q = 1. We discussed about the stability for the system of differential equations and found that the model is stable by the Routh-Hurwitz criterion.
Key-Words / Index Term
Mathematical Modelling, SIRS Model, Non-linear incidence rate, Stability
References
[1] Baily, N.T.J., The Mathematical Theory of Epidemics, Griffin, London (1975).
[2] Derrick, W.R. and Driessche, P. Van Den, A disease transmission model in a non-constant population, J. Math. Biol. 31(1993) 495-511.
[3] Driessche, P. Van Den and Watmough, J., r-k simple S1S epidemic model with a backward bifurcation, J. Math. Rio. 40 (2000) 525-540.
[4] Dushoff, J., Huang, W., Castillo-Chavez, C., Backwards bifurcations and catastrophe in simple models of fatal diseases, J. Math. Biol. 36 (1998) 227-248.
[5] Hethcote, H.W., The mathematics of infectious disease, SIAM Rev. 42 (2000) 599-653.
[6] Liu, W.M., Hethcote, H.W. and Levin, S.A., Dynamical behavior of epidemiological models with nonlinear incidence rates, J. Math. Biol. 25 (1987) 359-380,
[7] Lizana, M. and Rivero, J., Multiparametric bifurcations for a model in epidemiology, J. Math. Biol. 35.
[8] Wu, L., Feng, Z., Homoclinic bifurcation in at., SIQR model for childhood diseases, J. Differential Equations 168 (2000) 150-167.
Citation
Pradeep Porwal, "An SIRS Model with Disease Induced Death and Non- Linear Incidence Rate," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.3, Issue.3, pp.1-3, 2016