ABSTRACT
Society must understand, model, and forecast infectious disease transmission patterns in order to prevent pandemics. Mathematical models and computer technology may help us better understand the pandemic and create more systematic and effective infection management strategies. This study offers a novel perspective through a compartmental model that incorporates fractional calculus. The first scenario is based on proportional fractional definitions, considering compartmental individuals of susceptible, moving susceptible, exposed, infected, hospitalized, and recovered. Through an extension of this derivative, they decimated the model to integer order. We extended the deterministic model to a stochastic extension to capture the uncertainty or variance in disease transmission. It can develop an appropriate Lyapunov function to detect the presence and uniqueness of positive global solutions. Next, we discuss how the epidemic model might have become extinct. In our theoretical study, we demonstrated that a sufficiently outrageous amount of noise can cause a disease to become extinct. A modest level of noise, on the other hand, promotes the persistence of diseases and their stationary distribution. The Khasminskii method was used to determine the stationary distribution and ergodicity of the model.
ABSTRACT
A novel method for assessing the effectiveness of enrichment evaluations PROMETHEE combining pentagonal intuitionistic fuzzy numbers (PIFNs) and preference rank-ing organization is presented in the present paper. PIFN suggests a new technique for multi -criteria group decision making (MCGDM) in which two characteristic values of membership and non-membership functions are involved. The key practicality of incorporating PIFN in decision -making is its effective capability of managing the vagueness and uncertainties of linguistic terms used during discussions. The designed algorithm is then applied to get an appropriate, cost-effective, and publicly accepted awareness campaign to be used to forewarn populaces about any virulent disease, which has not been studied before. Importantly, it is the only way to protect any huge population of a country from any fatal disease, i.e. to be timely aware of the disease's transmissibility, severity, and precautionary measures through any effectively ap-proachable source. Here, we consider alternative sources of campaigns, such as commercial advertisement on television, on social media, on bills /other government circulars, billboards, and door-to-door volunteering for guidance. These alternative campaigns are based on five generalized criteria, where the weight of each criterion is evaluated via the fuzzy analytical hier-archy process (F-AHP). After using the F-AHP for complex decisions based on acceptance and effectiveness, the F-PROMETHEE algorithm is applied to achieve the closest ideal alternative.