QUALITATIVE ANALYSIS OF SEIRS ENDEMIC MODEL BOTH FROM PDEs AND ODEs PERSPECTIVE

An age-structured susceptible-exposed-infected-recovered-susceptible (SEIRS) endemic model is proposed in this analysis utilizing the tools of partial differential equations. Because of different outflows and inflows that are lopsided by migration and demographics factors, the population is supposed to be not constant. To demonstrate that the model is well-posed, an abstract Cauchy problem is developed from the proposed system. The simple reproduction number R-0 is used to analyze the local and global behavior of the disease-free equilibrium. The disease present equilibrium point is shown to exist and be stable locally under appropriate assumptions and conditions. We consider the age-free parameters and the problem is converted into an ordinary differential equations (ODEs) model. The ODEs model is investigated for disease-free and endemic equilibria and the global stability of each equilibrium is presented therein. A few simulations are carried out and discussed at the end of the paper to explain the central theorem of the study.