This study explores the onset of food allergies in individuals using antacid medications, employing an innovative fractional mathematical model integrating fractional calculus and differential equations. Through this methodology, we analyze the intricate dynamics of food allergy epidemics and their interaction with antacid usage, offering essential perspectives for refining management strategies and implementing early intervention measures. Our research stems from a 2001 case, marking the initial occurrence of a severe anaphylactic reaction to manioc, a novel food allergy. Prompted by the prolonged acknowledgment of incidents involving a tuber ingrained in native Brazilians’ diets for over 500 years, we establish a mathematical framework addressing the persistence of the cassava allergen in the presence of proton pump inhibitors (PPIs). These medications are utilized to reduce gastric acidity in digestive disorders, elevate pH levels, foster the preservation of the allergen and subsequently enhance immune recognition. Our investigation hinges on employing a mathematical model to scrutinize how incidents related to food allergies impact the dynamics of scientific publication. The model, offering a distinctive perspective on food allergy characterization, relies on a novel set of differential equations incorporating fractional Caputo-Fabrizio (CF) operators. Insights into the model’s long-term behavior are derived from a comprehensive examination of its qualitative characteristics and subsequent computational simulations. We establish the existence and uniqueness of solutions within the proposed model, drawing on established results concerning fixed points. Utilizing the Ulam-Hyers method, we determine stability outcomes. For in-depth numerical analysis and simulation, our study employs Newton’s polynomial in conjunction with the three-step Adams-Bashforth numerical technique. The findings underscore the efficacy of fractional order techniques in accurately capturing the complex dynamics of food allergies and providing insightful information crucial for devising effective management plans.

Computer networks can be alerted to possible viruses by using kill signals, which reduces the risk of virus spreading. To analyze the effect of kill signal nodes on virus propagation, we use a fractional-order SIRA model using Caputo derivatives. In our model, we show how a computer virus spreads in a vulnerable system and how it is countered by an antidote. Using the Caputo operator, we fractionalized the model after examining it in deterministic form. The fixed point theory of Schauder and Banach is applied to the model under consideration to determine whether there exists at least one solution and whether the solution is unique. In order to calculate the approximate solution to the model, a general numerical algorithm is established primarily based on Haar collocations and Broyden’s method. In addition to being mathematically fast, the proposed method is also straightforward and applicable to different mathematical models.

In this article, a stochastic SACR hepatitis B epidemic model is taken to be under consideration. We develop a stochastic epidemic model by considering the effect of environmental fluctuation on the hepatitis B dynamics and distribute the transmission rate by white noise. Using the stochastic Lyapunov function theory, we have shown the existence and uniqueness of the global positive solution. The extinction and persistence for our proposed model are derived with sufficient conditions. The numerical simulations are carried out using first-order Itô-Taylor stochastic scheme in the last section for the verification of our theoretical results.

This paper describes the existence and stability of the hepatitis B epidemic model with a fractional-order derivative in Atangana–Baleanu sense. Some new results are handled by using the Sumudu transform. The existence and uniqueness of the equilibrium solution are presented using the Banach fixed-point theorem. Moreover, sensitivity analysis complemented by simulations is performed to determine how changes in parameters affect the dynamical behavior of the system. The numerical simulations are carried out using a predictor-corrector scheme to demonstrate the obtained results.

We study the heat transfer of a Magneto Hydrodynamic (MHD) boundary layer flow of a Newtonian fluid over a pervious shrinking sheet under the influence of thermal slip. The flow allows electric current to pass through. The governing PDEs are transformed into self-similar ODEs via Lie group analysis. We study the variations in the dimensionless quantities like velocity and temperature of the flow in terms of the different parameters involved in the problem. We discuss the thickness of the boundary layers under the influence of various parameters involved in the flow. Numerical simulations are carried out to explain and support the results obtained.