Open AccessAn SEIRS Epidemic Model with Immigration and Vertical Transmission
Author(s) -
Ruksana Shaikh,
Pradeep Porwal,
Vandana Gupta
Publication year - 2020
Publication title -
asian research journal of mathematics
Language(s) - English
Resource type - Journals
ISSN - 2456-477X
DOI - 10.9734/arjom/2020/v16i1130241
Subject(s) - epidemic model , stability theory , stability (learning theory) , immigration , basic reproduction number , mathematics , mathematical economics , equilibrium point , transmission (telecommunications) , steady state (chemistry) , control theory (sociology) , economics , control (management) , mathematical analysis , physics , computer science , population , demography , law , sociology , chemistry , telecommunications , management , quantum mechanics , machine learning , political science , differential equation , nonlinear system
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.