Narrow Results

This paper establishes a new fractional frSIS model utilizing a continuous time random walk method. There are two main innovations in this paper. On the one hand, the model is analyzed from a mathematical perspective. First, unlike the classic SIS infectious disease model, this model presents the infection rate and cure rate in a fractional order. Then, we proved the basic regeneration number $R_0$ of the model and studied the influence of orders a and b on $R_0$. Second, we found that frSIS has a disease-free equilibrium point $E_0$ and an endemic equilibrium point $E^{\ast }$. Moreover, we proved frSIS global stability of the model using $R_0$. If $R_0<1$, the model of $E_0$ is globally asymptotically stable. If $R_0>1$, the model of $E^{\ast }$ is globally asymptotically stable. On the other hand, from the perspective of infectious diseases, we discovered that appropriately increasing a and decreasing b are beneficial for controlling the spread of diseases and ultimately leading to their disappearance. This can help us provide some dynamic adjustments in prevention and control measures based on changes in the disease.

This paper explores the necessary conditions required for the solutions of an integro-differential system of n-fractional differential equations (n-FDEs) in the modified-ABC case of derivative with initial conditions. The presumed problem is a linearly perturbed system. Some classical fixed point theorems are utilized to derive the solution existence criteria. Additionally, a numerical methodology utilizing Lagrange’s interpolation polynomial is developed and implemented in a dynamical framework of a power system for practical applications. In addition, we investigate the properties of Hyers–Ulam’s stability and uniqueness. The findings are evaluated using graphical methods to assess the precision and suitability of the approaches

In this work, we explore a new class of diffusion systems involving multi-term fractional integral operators and nonlinear coupling terms in a Hilbert space. First, we use a time semi-discrete approach grounded in the backward Euler difference formulation (i.e. Rothe’s method) to introduce a discrete iterative system. Then, the existence and uniqueness as well as the priori estimations of solution for the discrete iterative system are proved. Moreover, an approximating parabolic coupled system is considered, and an convergence result which shows that the solution of approximating coupled system converges to the unique strong solution of original problem, is obtained. Finally, we give three examples to illustrate the validity of the theoretical results.

Public health awareness programs have been a crucial strategy in mitigating the spread of emerging and re-emerging infectious disease outbreaks of public health significance such as COVID-19. This study adopts an Susceptible–Exposed–Infected–Recovered (SEIR) based model to assess the impact of public health awareness programs in mitigating the extent of the COVID-19 pandemic. The proposed model, which incorporates public health awareness programs, uses ABC fractional operator approach to study and analyze the transmission dynamics of SARS-CoV-2. It is possible to completely understand the dynamics of the model’s features because of the memory effect and hereditary qualities that exist in the fractional version. The fixed point theorem has been used to prove the presence of a unique solution, as well as the stability analysis of the model. The nonlinear least-squares method is used to estimate the parameters of the model based on the daily cumulative cases of the COVID-19 pandemic in Nigeria from March 29 to June 12, 2020. Through the use of simulations, the model’s best-suited parameters and the optimal ABC fractional-order parameter $\tau$ may be determined and optimized. The suggested model is proved to understand the virus’s dynamical behavior better than the integer-order version. In addition, numerous numerical simulations are run using an efficient numerical approach to provide further insight into the model’s features.