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Dynamics of SIR Model with Saturated Treatment Function under the Effect of Pollution

Naina Arya, Sumit Kaur Bhatia, Riya Jain


This paper studies SIR model with incidence rate which is saturated and nonlinear. We have considered saturated treatment function on a logistically growing population. Boundedness of the system has been obtained along with existence of disease-free and endemic equilibrium points. We deduce that the strict threshold for illness obliteration is weak when the basic reproduction number approaches unity. The global stability of the endemical equilibrium point is established using Lyapunov Lasalle theorem. Condition for Persistence of endemicity of our model has been discussed. Mathematically this paper recommends that keeping the atmosphere clean, building healthy relation with nature, giving timely treatment to the patients by increasing the equipment and capacity of hospitals, improving the cure
efficiency are all valid methods for managing the disease. Numerical simulations are shown that exhibit results obtained analytically.


Equilibrium Point, Saturated Treatment Function, Non Linear Incidence Rate, Bifurcation, Stability Analysis, Persistence.

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