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Infection with the hepatitis B virus (HBV) is a global health problem and may be controlled via appropriate treatment. We use fractional models to understand infectious diseases because fractional models help us understand treatments' effects on hepatitis B better than integer‐order models. In this article, we introduce a new mathematical model for HBV based on the fractal–fractional derivative with a generalized Mittag–Leffler kernel. Firstly, we discuss the fundamental properties, like the equilibria of the model and the primary reproduction number. Then, we investigate the existence of a unique solution to our model. We use an iterative method to solve the proposed model. Further, we discuss the stability of the model through stability theory. Finally, we offer some graphical illustrations for various values of the parameters. [ABSTRACT FROM AUTHOR]

Food security is a basic human right that guarantees humans an adequate amount of nutritious food. However, plant viruses and agricultural pests cause real damage to food sources, leading to negative impacts on meeting the human right of obtaining a sufficient amount of food. Understanding infectious disease dynamics can help us to design appropriate control and prevention strategies. Although cassava is among the most produced and consumed crops and greatly contributes to food security, cassava mosaic disease causes a decrease in photosynthesis and reduces cassava yield, resulting in a lack of crops. This paper developed a fractional model for cassava mosaic disease (CMD) dynamics based on the Caputo–Fabrizio (CF) fractional derivative to decrease cassava plant infection. We used fixed-point theory to study the existence of a unique solution in the form of the CMD model. A stability analysis of the model was conducted by using fixed-point theory and the Picard technique. A new numerical scheme was proposed for solving the nonlinear system of a fractional model in the sense of the CF-derivative and applied to obtain numerical simulations for a fractional model of the dynamics of CMD. The obtained results are described using figures that show the dynamics and behaviors of the compartments of CMD, and it is concluded that decreasing the population of whitefly vectors can prevent cassava plants from becoming infected better than increasing the recovery rate of the infected cassava plants. [ABSTRACT FROM AUTHOR]

ARS-CoV-2 can survive in different environments and remain infectious for several days, which presents challenges to eliminating infectious diseases. It encourages researchers to study the effects of SARS-CoV-2 on the environment. In this paper, we formulate an epidemic model for SARS-CoV-2, which focuses on the transmission of the virus under environmental conditions. Two distributed delays are introduced to describe the probability of the exposed and infected individuals in different infection periods based on the transmission of the virus in the environment. The positivity and boundness of solutions of model are derived. The basic reproduction number threshold theory is established and the results demonstrate that the persistence of COVID-19 depends on the basic reproduction number. Numerical simulations are presented to verify the theoretical results. Some measures are proposed to control and eliminate COVID-19 infectious diseases. [ABSTRACT FROM AUTHOR]

In this literature, we study the existence and stability of the solution of the boundary value problem of fractional differential equations with Φp-Laplacian operator. Our problem is based on Caputo fractional derivative of orders σ, ϵ, where k − 1 < σ, ϵ ≤ k, and k ≥ 3. By using the Schauder fixed point theory and properties of the Green function, some conditions are established which show the criterion of the existence and non-existence solution for the proposed problem. We also investigate some adequate conditions for the Hyers-Ulam stability of the solution. Illustrated examples are given as an application of our result. [ABSTRACT FROM AUTHOR]

The limitation of contact between susceptible and infected individuals plays an important role in decreasing the transmission of infectious diseases. Prevention and control strategies contribute to minimizing the transmission rate. In this paper, we propose SIR epidemic model with delayed control strategies, in which delay describes the response and effect time. We study the dynamic properties of the epidemic model from three aspects: steady states, stability and bifurcation. By eliminating the existence of limit cycles, we establish the global stability of the endemic equilibrium, when the delay is ignored. Further, we find that the delayed effect on the infection rate does not affect the stability of the disease-free equilibrium, but it can destabilize the endemic equilibrium and bring Hopf bifurcation. Theoretical results show that the prevention and control strategies can effectively reduce the final number of infected individuals in the population. Numerical results corroborate the theoretical ones. [ABSTRACT FROM AUTHOR]