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 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 and unstable when . 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.

Nowadays, coronavirus disease 2019 (COVID-19) poses a major threat to humanity which is caused by a novel coronavirus in Wuhan, China, at the end of December 2019. This novel coronavirus named the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) according to the International Committee on Taxonomy of Viruses (ICTV). It spreads directly through close contact with an asymptomatic (carrier) or symptomatic person who is coughing, sneezing, talking, singing and kissing. It also spreads indirectly through contact with an environment contaminated by viral particles of SARS-COV-2. In the absence of effective treatment against COVID-19, awareness can play an important role in reducing cases of COVID-19. In this study, we develop a mathematical model to better describe the dynamics of COVID-19 by taking into account the above modes of transmission and the prosocial awareness. The existence, uniqueness, positivity and boundedness of solutions of the model are discussed. All possible equilibrium points are determined. The local asymptotic stability of these equilibrium points is studied. Suitable Lyapunov functionals are constructed to investigate the global dynamics of the model.

Since the first outbreak in Wuhan, China, in December 31, 2019, COVID-19    pandemy  ‎has been spreading to many countries in the world. The ongoing COVID-19 pandemy 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 epidemy are immigration, travelers, foreign workers, and foreign students. In this work, we develop a mathematical model to study the dynamical ‎behavior of COVID-19 pandemy, 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.

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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.