In this paper, we consider a networked fractional SIR MODEL. After proving the existence and uniqueness of the solution, we obtain the basic reproduction number, the disease-free equilibrium point and the endemic equilibrium point. By constructing the Lyapunov function, we show that the endemic equilibrium is globally asymptotically stable when the basic reproduction number is greater than 1, and the disease-free equilibrium is globally asymptotically stable when the basic reproduction number is less than 1. Finally, numerical simulations are carried out to verify these theoretical results. Thus, the stability theory of Laplacian diffusion is extended to the graph Laplacian MODEL.

Finding the location for plans like factories or warehouses for any organization is an important and strategic decision. Costs of transportation which are the main part of the price of the goods, is the function of the location of these projects. to find the optimum location of these projects, there have been various methods proposed which are usually defined (not random). In reality and in dealing with real world conditions, taking into account influential and effective parameters leads to unexpected results. In this research, while introducing these defined algorithms, it been tried to random location MODEL based on the existing MODELs. Regarding this, by studying the MODELs taken in random location we tried to propose an efficient and effective MODEL. For this purpose, by using randomized planning and randomized constrained planning, we turn random MODEL to defined MODEL, which is solvable by using the last algorithm or standard planning methods.

Background: The Coronavirus 2019-nCOV (COVID-19) epidemic by SARS-CoV-2 is spreading worldwide, and by March 1, 2020, 67 countries, including Iran, have been affected. Many studies are being conducted at home and abroad to predict the outbreak of the disease so that they can make the necessary medical and health decisions in a timely manner. Methods: we used the SIR MODEL to identify parameters to calculate epidemic features and some estimates of the new coronavirus. Data on the transmission of the novel coronavirus were extracted from the GitHub source in the covid19. analytics software package. Results: According to our MODEL estimates, the rate of infection β = 1 and the rate of removal γ = 0. 667 and index R0 = 1. 497 were obtained. Because the value of R0 is more than one, it is still an epidemic disease. Given that tfinal~132 days was estimated, we can expect the transmission of this epidemic to stop in Iran after July 3, 2020, provided that existing quarantine measures and patient isolation rates continue as usual. In comparison with the global SIR MODEL, we reached the peak of the infection earlier than the global MODEL, but in improved and susceptible cases, we performed better than the global MODEL. The graph of recovered and susceptible cases in Iran earlier than the global MODEL cut off themselves. Conclusion: Forecasts are set to be a useful guide for deciding whether to transfer COVID-19. According to the predictions and estimates made, more attention should be paid to control measures.