NUMERICAL RESULTS FOR EPIDEMIOLOGICAL MODELS OF SIR AND SIS WITH REPLACEMENT NUMBERS
S. BALAMURALITHARAN *
Department of Mathematics, Faculty of Engineering and Technology, SRM University, Kattankulathur - 603 203, Tamil Nadu, India
*Author to whom correspondence should be addressed.
We introduce ordinary differential equation (ODE) models of the epidemic system designed for the study of the susceptible infectious recovered (SIR) and susceptible infectious susceptible (SIS) administration. The aim of this research work is to study alternative parameter estimation that would minimize the use of SIR and SIS using a mathematical modeling. The first model we propose is a parameter estimation model that considers SIS administration for population size, a dynamical disorder characterized by simple epidemic model in the replacement number. The second model develops the basic reproductive ratio solution for the SIR and a sufficient condition for the equilibrium. For each model, we use a combination of mathematical analysis and numerical simulations to study alternative epidemic models that would be efficient while reducing the parameter estimation.
Keywords: Contact number, replacement number, SIS, SIR