An SEIRS Epidemic Model with Immigration and Vertical Transmission
Ruksana Shaikh *
School of Studies in Mathematics, Vikram University, Ujjain, India.
Pradeep Porwal
School of Studies in Mathematics, Vikram University, Ujjain, India.
V. K. Gupta
Department of Mathematics, Govt. Madhav Science College, Ujjain, India.
*Author to whom correspondence should be addressed.
Abstract
The study indicates that we should improve the model by introducing the immigration rate in the model to control the spread of disease. An SEIRS epidemic model with Immigration and Vertical Transmission and analyzed the steady state and stability of the equilibrium points. The model equations were solved analytically. The stability of the both equilibrium are proved by Routh-Hurwitz criteria. We see that if the basic reproductive number R0<1 then the disease free equilibrium is locally asymptotically stable and if R0<1 the endemic equilibrium will be locally asymptotically stable.
Keywords: Mathematical modeling, immigration rate, vertical transmission, stability analysis, routh-hurwitz criteria.