An improved method of global dynamics: Analyzing the COVID-19 model with time delays and exposed infection.

Considering the transmission characteristics of the coronavirus disease 2019 (COVID-19), there are certain time delays in the transition from susceptible individuals to exposed individuals after contact with exposed, symptomatically infected, and asymptomatically infected individuals. A COVID-19 model with time delays and exposed infection is developed and then the global dynamics of this model is investigated by an improved method; moreover, the numerical simulations are carried out. It is shown that the COVID-19-free equilibrium T0 is globally asymptotically stable (GAS) if and only if the control reproduction number Rc≤1, while T0 is unstable and the COVID-19 equilibrium T∗ is GAS if and only if Rc>1. The numerical results reveal that strengthening quarantine measures is helpful to control the COVID-19 epidemic in India. Furthermore, when Rc<1, the numbers of symptomatically infected, asymptomatically infected, and quarantined individuals eventually tend to the zero equilibrium state, and with the increase in the time delay, the three kinds of variables change faster and their peaks become larger; when Rc>1, the three kinds of variables eventually tend to the positive equilibrium state, which are oscillatory and the amplitudes of the oscillation enlarge as the value of time delay increases. The numerical results show that when Rc<1, the smaller the value of time delay, the smaller the final epidemic size. In short, the longer it takes time for susceptible individuals to transform exposed individuals, the harder COVID-19 will be controlled.

Modeling COVID-19 transmission dynamics incorporating media coverage and vaccination.

The COVID-19 pandemic has caused widespread concern around the world. In order to study the impact of media coverage and vaccination on the spread of COVID-19, we establish an SVEAIQR infectious disease model, and fit the important parameters such as transmission rate, isolation rate and vaccine efficiency based on the data from Shanghai Municipal Health Commission and the National Health Commission of the People's Republic of China. Meanwhile, the control reproduction number and the final size are derived. Moreover, through sensitivity analysis by PRCC (partial rank correlation coefficient), we discuss the effects of both the behavior change constant $ k $ according to media coverage and the vaccine efficiency $ \varepsilon $ on the transmission of COVID-19. Numerical explorations of the model suggest that during the outbreak of the epidemic, media coverage can reduce the final size by about 0.26 times. Besides that, comparing with $ 50\% $ vaccine efficiency, when the vaccine efficiency reaches $ 90\% $, the peak value of infected people decreases by about 0.07 times. In addition, we simulate the impact of media coverage on the number of infected people in the case of vaccination or non-vaccination. Accordingly, the management departments should pay attention to the impact of vaccination and media coverage.

Dynamic Analysis of a Stochastic SEQIR Model and Application in the COVID-19 Pandemic

In this study, a deterministic SEQIR model with standard incidence and the corresponding stochastic epidemic model are explored. In the deterministic model, the reproduction number is given, and the local asymptotic stability of the equilibria is proved. When the reproduction number is less than unity, the disease-free equilibrium is locally asymptotically stable, whereas the endemic equilibrium is locally asymptotically stable in the case of a reproduction number greater than unity. A stochastic expansion based on a deterministic model is studied to explore the uncertainty of the spread of infectious diseases. Using the Lyapunov function method, the existence and uniqueness of a global positive solution are considered. Then, the extinction conditions of the epidemic and its asymptotic property around the endemic equilibrium are obtained. To demonstrate the application of this model, a case study based on COVID-19 epidemic data from France, Italy, and the UK is presented, together with numerical simulations using given parameters. [ FROM AUTHOR] Copyright of Discrete Dynamics in Nature & Society is the property of Hindawi Limited and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full . (Copyright applies to all s.)

Evaluating the impact of the travel ban within mainland China on the epidemic of the COVID-19.

OBJECTIVES: The ongoing COVID-19 pandemic expanded its geographic distribution through the movement of humans and caused subsequent local outbreaks. Hence, it is essential to investigate how human mobility and travel ban affect the transmission and spatial spread while minimizing the impact on social activities and national economics. METHODS: We developed a mobility network model for spatial epidemics, explicitly taking into account time-varying inter-province and inner-province population flows, spatial heterogeneity in terms of disease transmission, as well as the impact of media reports. The model is applied to study the epidemic of the dynamic network of 30 provinces of mainland China. The model was calibrated using the publicly available incidence and movement data. RESULTS: We estimated that the second outbreak occurred approximately on February 24, 2020, and the cumulative number of cases as of March 15, 2020, increased by 290.1% (95% CI: (255.3%, 324.9%)) without a travel ban in mainland China (excluding Hubei and Tibet). We found that intra-province travel contributes more to the increase of cumulative number of cases than inter-province travel. CONCLUSION: Our quantitative and qualitative research results suggest that the strict travel ban has successfully prevented a severe secondary outbreak in mainland China, which provides solutions for many countries and regions experiencing secondary outbreaks of COVID-19.

Global dynamics of COVID-19 epidemic model with recessive infection and isolation.

In this paper, we present an SEIIaHR epidemic model to study the influence of recessive infection and isolation in the spread of COVID-19. We first prove that the infection-free equilibrium is globally asymptotically stable with condition R0<1 and the positive equilibrium is uniformly persistent when the condition R0>1. By using the COVID-19 data in India, we then give numerical simulations to illustrate our results and carry out some sensitivity analysis. We know that asymptomatic infections will affect the spread of the disease when the quarantine rate is within the range of [0.3519, 0.5411]. Furthermore, isolating people with symptoms is important to control and eliminate the disease.

Study on an SIHRS Model of COVID-19 Pandemic With Impulse and Time Delay Under Media Coverage.

Media coverage plays an important role in prevention and control the spread of COVID-19 during the pandemic. In this paper, an SIHRS model of COVID-19 pandemic with impulse and time delay under media coverage is established. The positive and negative emotions of public are considered by the impact of confirmed cases and medical resources. In order to restrain the negative information of public, the factor of policies and regulations with impulse and time delay is introduced. Furthermore, the system model is simulated and verified by the reported data of COVID-19 pandemic in Wuhan. The main results are as follows: (1) When the implementation rate of the negative information generated by the confirmed cases gradually reduced to 0.4 times, the cumulative confirmed cases will be significantly reduced to about 37000, indicating that the popularization of pandemic related media information should be broad; (2) When the implementation rate affected by the amount of policies and regulations information gradually increases to 3 times, the cumulative confirmed cases will be significantly reduced to about 28000, indicating that the policies and regulations information should be continuously and incrementally reported; (3) When the inhibition rate of policies and regulation information on negative information gradually increases to 3 times, the cumulative confirmed cases will also be significantly reduced to about 27000 cases, indicating that the targeted policies and regulations information has a significant impact on inhibiting the corresponding negative emotions.

Dynamics of an SIS network model with a periodic infection rate.

Seasonal forcing and contact patterns are two key features of many disease dynamics that generate periodic patterns. Both features have not been ascertained deeply in the previous works. In this work, we develop and analyze a non-autonomous degree-based mean field network model within a Susceptible-Infected-Susceptible (SIS) framework. We assume that the disease transmission rate being periodic to study synergistic impacts of the periodic transmission and the heterogeneity of the contact network on the infection threshold and dynamics for seasonal diseases. We demonstrate both analytically and numerically that (1) the disease free equilibrium point is globally asymptotically stable if the basic reproduction number is less than one; and (2) there exists a unique global periodic solution that both susceptible and infected individuals coexist if the basic reproduction number is larger than one. We apply our framework to Scale-free contact networks for the simulation. Our results show that heterogeneity in the contact networks plays an important role in accelerating disease spreading and increasing the amplitude of the periodic steady state solution. These results confirm the need to address factors that create periodic patterns and contact patterns in seasonal disease when making policies to control an outbreak.