Some remarks on a mathematical model of COVID-19 pandemic with health care capacity

In this paper, a SEIR model proposed in the article "Dynamic analysis of mathematical model with health care capacity for COVID-19 pandemic” by S. Çakan (2020) is analysed. The model describes COVID-19 pandemic spread affected by healthcare capacity and is expressed by a system of delay differential equations. To prove the local stability of stationary states, S. Çakan uses linearization technique, though she does this as if the equations did not depend on the delay. Additionally, it is shown that the crucial argument used by S. Çakan to prove boundedness of the solutions is not correct, which implies that the proofs of global stability in the original article are not correct either. In this paper, improved proofs of local and global stability of the stationary states are provided. For local stability of the stationary states a standard linearization technique is used. Global stability of the stationary states is proved based on Lyapunov's functionals. Although the functionals are the same as those proposed by S. Çakan, additional properties of the solutions (in the case of disease-free stationary state) and the functional (in the case of the endemic stationary state) are proved. © 2022 Polish Mathematical Society. All rights reserved.

Global asymptotic stability of a delay differential equation model for SARS-CoV-2 virus infection mediated by ACE2 receptor protein.

The COVID-19 pandemic has brought a serious threat to human life safety worldwide. SARS-CoV-2 virus mainly binds to the target cell surface receptor ACE2 (Angiotensin-converting enzyme 2 ) through the S protein expressed on the surface of the virus, resulting in infection of target cells. During this infection process, the target cell ACE2 receptor plays a very important mediating role. In this paper, a delay differential equation model containing the mediated effect of target cell receptor is established according to the mechanism of SARS-CoV-2 virus invasion of target cells, and the global stability of the infection-free equilibrium and the infected equilibrium of the model is obtained by using the basic reproduction number  ℛ 0  and constructing the appropriate Lyapunov functional. The expression of the basic reproduction number  ℛ 0  intuitively gives the dependence on the expression ratio of the target cell surface ACE2 receptor, which is helpful for the understanding of the mechanism of SARS-CoV-2 virus infection.

Uniform Persistence and Global Attractivity in a Delayed Virus Dynamic Model with Apoptosis and Both Virus-to-Cell and Cell-to-Cell Infections

In this paper, we study the global dynamics of a delayed virus dynamics model with apoptosis and both virus-to-cell and cell-to-cell infections. When the basic reproduction number R0>1, we obtain the uniform persistence of the model, and give some explicit expressions of the ultimate upper and lower bounds of any positive solution of the model. In addition, by constructing the appropriate Lyapunov functionals, we obtain some sufficient conditions for the global attractivity of the disease-free equilibrium and the chronic infection equilibrium of the model. Our results extend existing related works.

Modelling the effects of media coverage and quarantine on the COVID-19 infections in the UK.

A new COVID-19 epidemic model with media coverage and quarantine is constructed. The model allows for the susceptibles to the unconscious and conscious susceptible compartment. First, mathematical analyses establish that the global dynamics of the spread of the COVID-19 infectious disease are completely determined by the basic reproduction number R0. If R0 ≤ 1, then the disease free equilibrium is globally asymptotically stable. If R0 > 1, the endemic equilibrium is globally asymptotically stable. Second, the unknown parameters of model are estimated by the MCMC algorithm on the basis of the total confirmed new cases from February 1, 2020 to March 23, 2020 in the UK. We also estimate that the basic reproduction number is R0 = 4.2816(95%CI: (3.8882, 4.6750)). Without the most restrictive measures, we forecast that the COVID-19 epidemic will peak on June 2 (95%CI: (May 23, June 13)) (Figure 3a) and the number of infected individuals is more than 70% of UK population. In order to determine the key parameters of the model, sensitivity analysis are also explored. Finally, our results show reducing contact is effective against the spread of the disease. We suggest that the stringent containment strategies should be adopted in the UK.