(Asian Journal of Pure and Applied Mathematics, 2021-09) Olopade, Adesola I.; Adesanya, Adelani O.; Akinwumi, Titilayo O.
The SEIR mathematical and epidemiological model with natural immunity and treatment rate are
explored in this paper. Both local and global stability were analyzed for disease-free equilibrium point.
The threshold quantity “Basic Reproduction Number” ( 0 R ) with natural immunity was derived using
next generation matrix method (NGM), and it is shown that the disease free equilibrium point is locally
and globally asymptotically stable whenever the basic reproduction number is less than unity i.e. (
R0 1), while endemic whenever ( 1 0 R ). Numerical simulations show that, strong natural immunity
reduces the dynamical spread of epidemic diseases.