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

Ismael Khorshed Abdulrahman

The model used in the previous section was based on the mathematical model of the problem. We can also build a machine-learning program to simulate the same system using the input and output data of the model. Simulink provides the user with an adaptive neuro-fuzzy inference system (ANFIS) toolbox to generate if-then fuzzy rules automatically based on training the given data. References [18] present a detailed description of this technique in which the same methodology is employed in this paper. Using a basic SIR model built in Simulink with a variable infection rate and constant recovery rate, the model is trained using input-out data. The input could be the infection rate, recovery rate, or a combination of the two. The output could be the infectious output or its cumulative function. In this study, the beta function and its derivative are used as input variables to the ANFIS model whereas the infectious and cumulative infectious variables are chosen for the output in two different training processes. ANFIS allows us to use only one output for each block and for this reason, two separate processes are used to generate two ANFIS blocks for the two outputs. More outputs require more ANFIS blocks. Figure 7 shows a simple Simulink program used in this training. The recovery function is treated as constant as proposed in [6] whereas the infection rate is treated as variable [6] . With the parameters optimized, the ANFIS toolbox is used to generate seven fuzzy rules for each output. The membership function used in this training is the gaussian function. Figure 8a -c shows the training iterations, fuzzy rules, and the ANFIS outputs for the cumulative and infectious variables. Figure 9 shows the Simulink model for the ANFIS blocks used in this simulation. These if-then rules are used to simulate the case of China outbreak and the results are shown in Fig. 10a . whereas Fig. 10b shows the infections and recovery parameter values. Notably, the results show some good matching but it needs improvement. A more detailed and complicated beta function formula can be used to improve the accuracy of the results.