Mathematical Transmission of SEIR Epidemic Model with Natural Immunity
Adesola I. Olopade *
Department of Mathematics and Statistics, Federal University Wukari, P.M. B. 1020, Wukari, Taraba State, Nigeria.
Adelani O. Adesanya
Department of Mathematics and Computer Science, Elizade University, P.M.B. 002, Ilara-Mokin, Ondo State, Nigeria.
Titilayo O. Akinwumi
Department of Mathematics and Computer Science, Elizade University, P.M.B. 002, Ilara-Mokin, Ondo State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
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” ( ) 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. ( ), while endemic whenever ( ). Numerical simulations show that, strong natural immunity reduces the dynamical spread of epidemic diseases.
Keywords: Dermatoglyphics, Epidemic, Muria gonds, basic reproduction number, Bastar tribes, stability, natural immunity, treatment