Since Kermack and McKendrick delivered their well-known epidemiological SIR model in 1927, mathematics of infectious diseases has grown as an interdisciplinary studies area together with expertise from biology, computer science, and mathematics. Due to current threatening epidemics inclusive of COVID-19, this interest is constantly rising. As our essential goal, we establish an implicit time-discrete SIR (prone people–infectious people–recovered people) version. For this purpose, we first introduce its non-stop version with time-various transmission and healing prices and, as our first contribution, discuss thoroughly its properties. With admiration to those results, we develop different possible time-discrete SIR fashions, we derive our implicit time-discrete SIR model in comparison to many different works which specifically look into specific time-discrete schemes and, as our essential contribution, display precise solvability and similarly suited properties compared to its continuous version. We very well display that among the favored residences of the time-continuous case are still legitimate in the time-discrete implicit case. Especially, we show an upper error sure for our time-discrete implicit numerical scheme. Finally, we observe our proposed time-discrete SIR version to currently to be had data concerning the spread of COVID-19 in Germany and Iran.

The distribution fitting, time collection modeling predictive tracking processes, and mathematics of infectious diseases epidemiological modeling are illustrated. When the epidemiology data is enough to be in shape with the specified pattern size, the everyday distribution in general or other theoretical distributions are fitted and the best-fitted distribution is selected for the prediction of the spread of the disorder. The infectious illnesses increase over the years and we’ve statistics on the single variable this is the variety of infections that happened, therefore, time collection models are fitted and the prediction is done primarily based totally on the best-outfitted version. Monitoring processes can also be carried out to time collection fashions that can estimate the parameters greater precisely. In epidemiological modeling, greater organic parameters are incorporated into the fashions and the forecasting of the disorder unfold is carried out. We came up with, how to enhance the prevailing modeling methods, using fuzzy variables, and detecting fraud in the available statistics. Ultimately, we’ve reviewed the results of recent statistical modeling efforts to expect the course of COVID-19 to unfold.