Mathematical Modeling and Analysis for COVID-19 Model by Using Implicit-Explicit Rung-Kutta Methods

Abstract

One of the most common health care problems globally is COVID-19, and also there are an international effort to monitor it have been proposed and discussed. Despite the fact that many studies have been performed based on clinical evidence and confirmed infected cases. However, there is room for additional research since a range of complex criteria are included for later research forecast. As a consequence, mathematical modelling mixed with the numerical simulations is an effective method for estimating main propagation parameters and forecasting disease model dynamics. We study and present some models for the COVID-19 in this paper, which can answer significant questions concerning global health care and implement important notes. The IMEX Runge–Kutta and classical Runge–Kutta methods are two well-known computational schemes to find the solution for such system of differential equations. The results, which are based on these numerical procedures suggested and provide estimated solutions, provide critical answers to this global problem. The amount of recovered, infected, susceptible, and quarantined people in the expectation can be estimated using numerical data. The findings could also aid international efforts to increase prevention and strengthen intervention programs. The findings could also support international efforts to increase prevention and strengthen intervention programs. It is clearly that the proposed methods more accurate and works in a very large interval in time with a few step sizes. That is consequently beginning to a decrease in the computational price of the method. Numerical experiments show that there is a good argument and accurate solutions for solving this type of problem.

Simulating the COVID-19 Epidemic: A Numerical Examination of SIR, SIRID, and SIRVI Models

“…This spread results from contaminated contact between the infected population and the healthy population, and the number of infected individuals increases as a function of the number of contaminated contacts between infected individuals and healthy individuals. This number is proportional to the size of the infected population and the size of the healthy population, and therefore to the product of these two numbers, I*S. Therefore, we can write [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]:…”

“…Symmetrically, the size of the susceptible population decreases. Therefore, it can be written [15][16][17][18][19]:…”

“…If an individual stays on average λ days, I/λ is the instantaneous value of the flow between the "infected" compartment and the "recovered" compartment, i.e., the measure of the flow of individuals who recover, leaving the "infected" compartment, towards the "recovered" compartment. This action governing infected individuals, which we can write as [15][16][17][18][19]:…”

“…The number of recovered individuals I/λ of the healed individuals [15][16][17][18][19], where γ=1/λ.…”

Model Reduction and Analysis for ERK Cell Signalling Pathway Using Implicit-Explicit Rung-Kutta Methods

“…In addition, we propose a method to avoid the difficulties that appear when the models of ERK cell signalling pathway transfer to stiff nonlinear equations with an implicit method. This method is called Implicit -Explicit (IMEX) schemes for more details [12][13][14][15]. Consider the numerical method of the following system of stiff ordinary differential equation:…”