ANALYSIS OF AN SIRS EPIDEMIC MODEL WITH ASYMPTOTICALLY HOMOGENEOUS TRANSMISSION FUNCTION AND EMIGRATION RATE
SHIVRAM SHARMA *
School of Studies in Mathematics, Vikram University, Ujjain (M.P.), India
V. H. BADSHAH
School of Studies in Mathematics, Vikram University, Ujjain (M.P.), India
VANDANA GUPTA
Department of Mathematics, Govt. Kalidas Girls College, Ujjain (M.P.), India
*Author to whom correspondence should be addressed.
Abstract
In this paper, we derive an SIRS epidemic model with an asymptotically homogeneous transmission function and emigration rate. We obtain the disease free and endemic equilibrium. The sufficient conditions for the global stability of the equilibrium are also obtained. An example is also furnished which demonstrates validity of main result.
Keywords: SIRS model, transmission function, basic reproductive number, disease-free equilibrium, endemic equilibrium, stability