Modified Sirs Epidemic Model with Immigration and Saturated Incidence

Amit Kumar, Pardeep Porwal, V. H. Badshah


The present mathematical model deals with the study of SIRS epidemic model with immigration and saturation type incidence. We start from formulation of model and analyze it. The disease free equilibrium and endemic equilibrium of the system are established. If the DFE (Disease Free Equilibrium) is globally stable and if then the endemic equilibrium is obtained which is globally stable. An example also provides to justify the stability.

Full Text:



H.W. Hethcote and P. Vanden Driessch., “ Some epidemiological model with non-linear incidence,” Journal Math Biology, vol 29, 1991, pp. 271-287.

J.M. Mena Lorca. and H. W. Hethcote., “ Dynamic models of infectious disease as regulators of population sizes,” Journal Math Biology, vol 30, 1992, pp. 693-716.

L. Esteva and M.A. Matias, “ Model for vector transmitted diseases with saturation incidence,” Journal of Biology System, vol 9(4), 2001, pp. 235-245.

P. Porwal. and V.H. Badshah., “Modified epidemic model with saturated incidence rate and reduced transmission under treatment,” International Journal of Mathematics Archieve, vol 4(12), 2013, pp. 106-111.

P. Porwal., P. Ausif. and S.K. Tiwari., “ An sis model for human and bacterial population with modified saturated incidence rate and logistic growth.” International Journal of Modern Mathematical Science, vol 12(2), 2013, pp. 98-111.

P. Porwal. and V.H. Badshah., “Dynamical study of SIRS epidemic model with vaccinated susceptibility,” Canadian Journal of Basic and Applied Science, vol 2(04), 2014, pp. 90-96

P. Porwal., P. Shrivastava . and S.K. Tiwari., “ Study of single SIR epidemic model.” Pelagia Library, Advance in applied Science Research, vol 6(4), 2015, pp. 1-4.

R.M. Anderson and R.M. May, “Population biology of infection disease-I , Nature,” New York Springer Verlag, Berlin, 1979, pp .361-367.

S. Pathak., A. Maiti.,and G.P. Samanta., “ Rich dynamics of an sir epidemic model,” Non-linear Analysis Modeling and Control, vol 15(1), 2010, pp. 71-81.

V. Capasso. and G. Serio., “ A generalization of the kermack and mc Kendrick deterministic epidemic model,” Math Bio Science, vol 42, 1978, pp. 41-61.


  • There are currently no refbacks.

MAYFEB Journal of Mathematics 
Toronto, Ontario, Canada
ISSN 2371-6193