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In this research article, we investigated a coronavirus (COVID-19) epidemic model with random perturbations, which was mainly constituted of five major classes: the susceptible population, the exposed class, the infected population, the quarantine class, and the population that has recovered. We studied the problem under consideration in order to derive at least one, and only one, nonlocal solution within the positive feasible region. The Lyapunov function was used to develop the necessary result of existence for ergodic stationary distribution and the conditions for the disease's extinction. According to our findings, the influence of Brownian motion and noise effects on epidemic transmission were powerful. The infection may diminish or eradicate if the noise is excessive. To illustrate our proposed scheme, we numerically simulated all classes' findings.

The efficiency, temperature distribution, and temperature at the tip of straight rectangular, growing and decaying moving exponential fins are investigated in this article. The influence of internal heat generation, surface and surrounding temperatures, convection-conduction, Peclet number and radiation-conduction is studied numerically on the efficiency, temperature profile, and temperature at the tip of the fin. Differential transform method is used to investigate the problem. It is revealed that thermal and thermo-geometric characteristics have a significant impact on the performance, temperature distribution, and temperature of the fin's tip.The results show that the temperature distribution of decaying exponential and rectangular fins is approximately 15 and 7% higher than growing exponential and rectangular fins respectively. It is estimated that the temperature distribution of the fin increases by approximately 6% when the porosity parameter is increased from 0.1 to 0.5. It is also observed that the decay exponential fin has better efficiency compared to growing exponential fin which offers significant advantages in mechanical engineering.

In the present manuscript, an age-structured heroin epidemic model is formulated with the assumption that susceptibility and recovery are age-dependent. Keeping in view some control measures for heroin addiction, a control problem for further analysis is presented. The main results are the existence of control variables, sensitivities, adjoint system and the setting of an optimal control problem. We used the techniques of weak derivatives and a general principle of Pontryagin's type for obtaining the optimal control problem. To compare our results, we demonstrated sample simulations which show the effect of control on the entire population.

The current work is devoted to bring out a detail analysis including qualitative and semi-analytical study of Hepatitis B model under the Caputo- Fabrizio fractional derivative (CFFD). For the required results, fixed point theory is used to establish the conditions for existence and uniqueness of solution to the considered model. On the other hand, for semi analytical solutions, we use decomposition method of Adomian coupled with integral transform of Laplace. Moreover, the concerned solutions are presented via graphs to analyze the dynamics of different compartments of the model.

The pandemic of SARS-CoV-2 virus remains a pressing issue with unpredictable characteristics which spread worldwide through human interactions. The current study is focusing on the investigation and analysis of a fractional-order epidemic model that discusses the temporal dynamics of the SARS-CoV-2 virus in a community. It is well known that symptomatic and asymptomatic individuals have a major effect on the dynamics of the SARS-CoV-2 virus therefore, we divide the total population into susceptible, asymptomatic, symptomatic, and recovered groups of the population. Further, we assume that the vaccine confers permanent immunity because multiple vaccinations have commenced across the globe. The new fractional-order model for the transmission dynamics of SARS-CoV-2 virus is formulated via the Caputo-Fabrizio fractional-order approach with the maintenance of dimension during the process of fractionalization. The theory of fixed point will be used to show that the proposed model possesses a unique solution whereas the well-posedness (bounded-ness and positivity) of the fractional-order model solutions are discussed. The steady states of the model are analyzed and the sensitivity analysis of the basic reproductive number is explored. Moreover to parameterize the model a real data of SARS-CoV-2 virus reported in the Sultanate of Oman from January 1st, 2021 to May 23rd, 2021 are used. We then perform the large scale numerical findings to show the validity of the analytical work.