A MATHEMATICAL ANALYSIS OF THE SIR MODEL WITH HOLLING TYPE II FUNCTIONAL OCCURRENCE RATE AND TREATMENT RATE

In this paper, a SIR epidemic model is proposed with nonlinear inhibitory effect and saturated treatment rate. When deciding the threshold value for the disease and the model's dynamics, the basic reproduction number is determined. The requirements for the existence of all equilibrium points are known and we have also found that they depend on the conditions. In local and global terms, the stability of equilibrium is discussed. The stochastic version of the model was also formulated to take into account the effect of noise. Population variance intensities (fluctuations) around the positive point of equilibrium due to noise have been measured. Every attempt was made to present the numerical simulations we proposed for the model.It is explicitly expected that the theoretical results will be supported and tested.
Key words: Local Stability, Global Stability, SIR epidemic model.