In this article, we propose a novel mathematical model for the spread of COVID-19 involving environmental white noise. The new stochastic model was studied for the existence and persistence of the disease, as well as the extinction of the disease. We noticed that the existence and extinction of the disease are dependent on ${\mathcal{R}}_0$ (the reproduction number). Then, a numerical scheme was developed for the computational analysis of the model; with the existing values of the parameters in the literature, we obtained the related simulations, which gave us more realistic numerical data for the future prediction. The mentioned stochastic model was analyzed for different values of ${\sigma }_1,{\sigma }_2$ and ${\beta }_1,{\beta }_2$, and both the stochastic and the deterministic models were compared for the future prediction of the spread of COVID-19.

In recent decades, AIDS has been one of the main challenges facing the medical community around the world. Due to the large human deaths of this disease, researchers have tried to study the dynamic behaviors of the infectious factor of this disease in the form of mathematical models in addition to clinical trials. In this paper, we study a new mathematical model in which the dynamics of $\mathrm{CD}{4}^{+}$ T-cells under the effect of HIV-1 infection are investigated in the context of a generalized fractal-fractional structure for the first time. The kernel of these new fractal-fractional operators is of the generalized Mittag-Leffler type. From an analytical point of view, we first derive some results on the existence theory and then the uniqueness criterion. After that, the stability of the given fractal-fractional system is reviewed under four different cases. Next, from a numerical point of view, we obtain two numerical algorithms for approximating the solutions of the system via the Adams-Bashforth method and Newton polynomials method. We simulate our results via these two algorithms and compare both of them. The numerical results reveal some stability and a situation of lacking a visible order in the early days of the disease dynamics when one uses the Newton polynomial.

In the present work, an unsteady convection flow of Casson fluid, together with an oscillating vertical plate, is examined. The governing PDEs corresponding to velocity and temperature profile are transformed into linear ODEs with the help of the Laplace transform method. The ordinary derivative model generalized to fractional model is based on a generalized Fourier law. The solutions for energy and velocity equations are obtained after making the equations dimensionless. To check the insight of the physical parameters, especially the symmetric behavior of fractional parameters, it is found that for small and large values of time, fluid properties show dual behavior. Since the fractional derivative exhibits the memory of the function at the chosen value of time, therefore the present fractional model is more suitable in exhibiting memory than the classical model. Such results can be useful in the fitting of real data where needed. In the limiting case when fractional parameters are taken $\beta =\gamma$ = 0 and $\alpha$ = 1 for both velocity and temperature, we get the solutions obtained with ordinary derivatives from the existing literature.

In this paper, we establish a new integral identity involving differentiable functions, and then we use the newly established identity to prove some Ostrowski–Mercer-type inequalities for differentiable convex functions. It is also demonstrated that the newly established inequalities are generalizations of some of the Ostrowski inequalities established inside the literature. There are also some applications to the special means of real numbers given.

In this paper, we prove the sufficient conditions for the existence results of a solution of a nonlocal q-symmetric integral boundary value problem for a sequential q-symmetric integrodifference equation by using the Banach’s contraction mapping principle and Krasnoselskii’s fixed point theorem. Some examples are also presented to illustrate our results.

Background Group A streptococcus (GAS) is the most frequent cause of bacterial pharyngitis in school-aged children. The postinfection sequel as acute rheumatic fever (ARF) and rheumatic heart disease that cause morbidity and mortality among young people is public health concerns in several developing countries. Asymptomatic carriage state of GAS is not fully understood in terms of host and bacterial factors. Although the ability of transmitting GAS of the asymptomatic carriers is relatively low, they may present the reservoir of the epidemic. A fraction of GAS carriers is difficult to estimate in practice and may greatly vary between populations. Understanding the role of carriage on the transmission dynamic of GAS is important for assessing the public health impact of the ARF. Method This study investigates the effect of GAS carriers on both the transmission and dynamic of ARF cases by using a mathematical model. Result We derive the sufficient conditions for which the GAS can spread or extinct from the naive population under the variation of the fraction of symptomatic cases over the incidence of GAS. The threshold is possible to occur in general, but the last condition which is rather restrictive and involves parameter uncertainty. The increasing of carriers in the endemic state leads to the reduction in magnitude of the reproduction number and the number of ARF patients. We demonstrate that the adjustment of parameters can be carried out by the use of endemic state and some specific data. Conclusion We show theoretically that the presence of asymptomatic carriers may induce the epidemic threshold and reduce the virulence of GAS and the prevalence of ARF.