SimCOVID: An Open-Source Simulink-Based Program for Simulating the COVID-19 Epidemic

Ismael Khorshed Abdulrahman

It is advantageous to have an educational program that displays the mathematical model of the epidemic in a visualized block diagram instead of a coded script. One of the widely-used platforms for studying the dynamic behavior of a system is Simulink. It has been used by many academic researchers in different fields for simulating a system using time-domain simulations. A dynamic system, such as the COVID-19 epidemic, can be mathematically modeled by a set of differential equations (DEs) or a set of differential-algebraic equations (DAEs) depending on the employed model. Simulink provides the user with useful mathematical tools including parameter estimation and system optimization which are needed in simulating a pandemic such as COVID-19. Simulink allows the user to enter and plot the confirmed cases of infection of the disease as an input to the system and then compute the system parameters (for instance, infection rate, recovery rate, etc.) so that the output of the simulation and the collected actual data are equals or very close to each other. This paper presents an open-source program for tracking, estimating, and simulating the coronavirus outbreak. Unlike the existing models, the mathematical model of the outbreak is represented and visualized as a block diagram in Simulink using SIR and SEIRD representation. The infection and recovery rate functions are treated as a constant, variable, or a combination of them. With the application of the adaptive neuro-fuzzy inference system (ANFIS), the outbreak of China and Italy are implemented in Simulink using both a standard mathematical model and ANFIS system. 1.1 SIR, SEIR, and SIRD models SIR model is a basic representation used widely to describe a disease spread, and it is the fundamental model for the other models such as SEIR and SIRD. SIR model consists of threecompartment levels: Susceptible, Infectious, and Removed. Any individual belongs to one of these groups. A brief description of these compartments is given below. Susceptible individuals are those people who have no immunity to the disease but they are not infectious. Since there is no vaccine yet developed for this disease, we can say that the entire community is exposed to get infected by this disease and hence, the "Susceptible" compartment can be represented by the entire population. An individual in the "Susceptible" level can move into the next level of the model (Infectious) through contact SimCOVID: An Open-Source Simulation Program for the COVID-19 Outbreak C 1 with an infectious person. By this single transmission, the number of susceptible\infectious people reduces\increases by one, respectively. The next group of people is for the infectious people who have the disease and can spread it to susceptible people. Infectious people can move to the "Removed" compartment by recovering from the disease. The removed compartment includes those who are no longer infectious and the ones who have dies from the disease (closed cases). The summation of these three compartments in the SIR model remains constant and equals the initial number of population. A basic SIR model is shown in Fig. 1 , where denotes the infection rate or the transmission rate or the force of infection, and denotes the recovery or removed rate. Generally speaking, these parameters ( , ) are not constant; they are functions of the size of infectious and recovery compartments. These are the parameters that we want to optimize and estimate so that the rep