Fuzzy mathematical modelling on diabetic and non-diabetic cases after vaccination

The COVID-19 is contagious and menacing, it is more obscure in identifying the infections in primary stage as it able to thrive in both hot and cold conditions. So, in this paper we have developed the Susceptible Vaccinated Infected Recovered (SVIR) model utilising the Michaelis-Menten Functional Response to explain the infections of COVID-19 especially for diabetic who are having more chances of getting infected as they are already vulnerable due to their lack of immunity. We also considered non-diabetic patients and discussed the symptomatic and asymptomatic infections for both diabetic and non-diabetic patients as well as the recuperation from COVID-19 (Coronavirus Disease). We have found the uncertainty in the rate of change variables, so we used the fuzzy concept to lower the uncertainty and find a better model. For this environment, we have used Trapezoidal Numbers(TFN) and fuzzified the rate of change variables and by using the Partition Defuzzification Method(PDM) we defuzzified the values and got accurate results. Additionally, using Python programming, we compared the variations between the crisp and fuzzy models and we also discussed the equilibrium points, performed sensitivity analysis, and examined the stability of the model.