A Numerical Study of SIR Epidemic Model

N. Kousar, R. Mahmood, M. Ghalib


Epidemic and infectious disease fall into the category of time dependent dynamic system. The model under consideration is SIR-type (susceptible, infectious, recovered) which assumes that every individual has equally chances to be infected by the infectious individual in the case of contact except the pair formation or those who have a sufficient immunity for the disease. The model considered in this paper is non-fatal. If the portion of the immuned population exceeds the herd immunity level then the disease will no longer persist in the population. The model is solved with and without demographical effects. The vaccination effect is also discussed along with the physical parameters. The simulations have been performed for the non-linear coupled ordinary differential equations using Runge-Kutta 4th order method and MATLAB-SIMULINK software. The results obtained by both methods are in good agreement with the existing results in the literature [7].


SIR Epidemic Model; Simulink; Runge-Kutta Method.

Full Text:



Beretta E, Takeuchi Y. (1995). Global stability of an SIR model with time delays. J Math Biology. 33:250260.

Keeling and Grenfell. (1997). Disease Extinction and Community size: modeling and persistence of measles. Science 275, 65-67.

Andersson, H., Britton, T., 2000. Stochastic epidemics in dynamic populations: quasi-stationarity andextinction. J. Math. Biol. 41, 559580.

Lloyd, A.L. ( 2001a) Destabilization of epidemic models with the inclusion of realistic distributions of infections periods. Proc. R. Soc. London B 268, 985993.

Lloyd, A.L. (2001b). Realistic distributions of infectious periods in epidemic models: changing patterns of persistence and dynamics. Theor. Popul. Biol. 60, 5971.

H Trottier, P Philippe. (2000). Deterministic Modeling of Infectious Diseases: Theory and Methods. The Internet Journal of Infectious Diseases, 1(2).

F. Awawdeh, A. Adawi, Z. Mustafa. (2009). Solutions of the SIR model of epidemics using HAM. Chaos, Solitons and Fractals 42, 30473052.


  • There are currently no refbacks.





About IJSBAR | Privacy PolicyTerms & Conditions | Contact Us | DisclaimerFAQs 

IJSBAR is published by (GSSRR).