A modified susceptible-infected-recovered epidemiological model - Bica, Ion; Zhai, Zhichun; Hu, Rui (My University, 2022)
Objectives This paper proposes an infectious disease model incorporating two new model compartments, hospitalization, and intensive care unit. Methods The model dynamics are analyzed using the local and global stability theory of nonlinear systems of ordinary differential equations. For the numerical simulations, we used the Rosenbrock method for stiff initial value problems. We obtained numerical simulations using MAPLE software. The returned MAPLE procedure was called only for points inside the range on which the method evaluated the numerical solution of the system with specied initial conditions. Results We proposed a new model to describe the dynamics of microparasitic infections. Numerical simulations revealed that the proposed model fitted with the expected behaviour of microparasitic infections with "acute epidemicity." The numerical simulations showed consistency in the behaviour of the system. Conclusions The model proposed has "robust" dynamics, supported by the global stability of its endemic state and the consistency of the numerical simulations regarding the model's time evolution behaviour. The introduction of the hospitalization and intensive care unit compartments in the proposed model revealed that it is essential to consider such policies in the case of "acute epidemicity" of microparasitic infections.
Keywords: epidemiological models; Rosenbrock method