Impact of the infected population and nonlinear incidence rate on the dynamics of the SIR model

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This study proposes a dynamical epidemic model SIR incorporating a nonlinear saturated incidence and nonlinear recovery rates. The model considers the influence of available resources, the ratio of the infected population, and the decrease of interventions on the spread of infectious diseases. The use of a nonlinear incident rate as a monoid-type equation improves the study compared to a constant-type incident rate because the spread of infection is now determined by the force of the illness and the number of infected individuals available to disseminate the infection. The consideration of recovery rate, which includes the minimum and maximum feasible recovery rates and the amount of resources available for treatment, makes the research more advantageous. The conditions for the existence of the equilibria have been established. Furthermore, stability analysis and bifurcation have been carried out using Lyapunov’s direct method, the Routh–Hurwitz criterion, and Dulac’s creation under each set of conditions. A numerical simulation was conducted using MATLAB. As the value of the preventive measure increases, the results indicate a considerable decrease in the infected compartment. In addition, the recovered population is growing as more resources, such as oxygen cylinders, hospital beds, and vaccination doses, become available.