The prime objective of the current study is to propose a novel mathematical framework under the fractional-order derivative, which describes the complex within-host behavior of SARS-CoV-2 by taking into account the effects of memory and carrier. To do this, we formulate a mathematical model of SARS-CoV-2 under the Caputo fractional-order derivative. We derived the conditions for the existence of equilibria of the model and computed the basic reproduction number ${\mathcal{R}}_0$. We used mathematical analysis to establish the proposed model’s local and global stability results. Some numerical resolutions of our theoretical results are presented. The main result of this study is that as the fractional derivative order increases, the approach of the solution to the equilibrium points becomes faster. It is also observed that the value of ${\mathcal{R}}_0$ increases as the value of $\beta$ and ${\pi }_v$ increases.

In this paper, we build and analyze a mathematical model of COVID-19 transmission considering media coverage effects. Due to transmission characteristics of COVID-19, we can divided the population into five classes. The first class describes the susceptible individuals, the second class is exposed individuals, the third class is infected individuals, the fourth class is quarantine class and the last class is recovered individuals. The existence, uniqueness and boundedness of the solutions of the model are discussed. The basic reproduction number ℛ0 is obtained. All possible equilibrium points of the model are investigated and their local stability is discussed under some conditions. The disease-free equilibrium is local asymptotically stable when ℛ0<1 and unstable when ℛ0>1. The globally asymptotical stability of all point is verified by Lyapunov function. Finally, numerical simulations are carried out to confirm the analytical results and understand the effect of varying the parameters on spread of COVID-19. These findings suggested that media coverage can be considered as an effective way to mitigate the COVID-19 spreading.

The emergence of novel RNA viruses like SARS-CoV-2 poses a greater threat to human health. Thus, the main objective of this article is to develop a new mathematical model with a view to better understand the evolutionary behavior of such viruses inside the human body and to determine control strategies to deal with this type of threat. The developed model takes into account two modes of transmission and both classes of infected cells that are latently infected cells and actively infected cells that produce virus particles. The cure of infected cells in latent period as well as the lytic and non-lytic immune response are considered into the model. We first show that the developed model is well-posed from the biological point of view by proving the non-negativity and boundedness of model’s solutions. Our analytical results show that the dynamical behavior of the model is fully determined by two threshold parameters one for viral infection and the other for humoral immunity. The effect of antiviral treatment is also investigated. Furthermore, numerical simulations are presented in order to illustrate our analytical results.

The aims of this paper is investigating the spread of AIDS both within-host, through the contact between healthy cells with free virus inside the body, and between-host, through sexual contact among individuals and external sources of infectious. The outbreak of AIDS is described by a mathematical model consisting of two stages. The first stage describes the within-host spread of AIDS and is represented by the first three equations. While the second stage describes the between-host spread of AIDS and represented by the last four equations. The existence, uniqueness and boundedness of the solution of the model are discussed and all possible equilibrium points are determined. The local asymptotic stability (LAS) of the model is studied, while suitable Lyapunov functions are used to investigate the global asymptotic stability (GAS) of the model. Optimal control strategy is used to control the outbreak of AIDS. Finally, a numerical simulation is carried out to confirm the analytical results and understand the effects of varying the parameters on the spread of disease.

‎ Since the first outbreak in Wuhan, China, in December 31, 2019, COVID-19 pandemic ‎has been spreading to many countries in the world. The ongoing COVID-19 pandemic has caused a ‎major global crisis, with 554,767 total confirmed cases, 484,570 total recovered cases, and ‎‎12,306 deaths in Iraq as of February 2, 2020. In the absence of any effective therapeutics or drugs ‎and with an unknown epidemiological life cycle, predictive mathematical models can aid in ‎the understanding of both control and management of coronavirus disease. Among the important ‎factors that helped the rapid spread of the epidemic are immigration, travelers, foreign workers, and foreign students. In this work, we develop a mathematical model to study the dynamical ‎behavior of COVID-19 pandemic, involving immigrants' effects with the possibility of re-infection. ‎Firstly, we studied the positivity and roundedness of the solution of the proposed model. The stability ‎results of the model at the disease-free equilibrium point were presented when . Further, it was proven that the pandemic equilibrium point will persist uniformly when . Moreover, we ‎confirmed the occurrence of the local bifurcation (saddle-node, pitchfork, and transcritical). Finally, ‎theoretical analysis and numerical results were shown to be consistent.