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China is one of the countries in the world carrying a heavy burden of tuberculosis. Due to the unbalanced economic development, the number of people working in other parts of country is huge, and the mobility of personnel has exacerbated the increase in tuberculosis cases. Most patients affected by this are in their middle and young ages. It is having a great impact among the family and society. Therefore, research on how to control this disease is absolutely necessary. The population is divided into two categories such as local population and the immigrant population. A pulmonary tuberculosis dynamic model with population heterogeneity is established. We calculate the basic reproductive number and the controlled reproductive number, and discuss the two types of population under the constraints given by the amount of vaccine and the optimal immunization ratio obtained is (0. 1 1 8 , 0. 1 0 7) , which can reduce the effective reproduction number from 5.85 to 0.227. It is understood that immunizing the local population will control the spread of the epidemic to a large extent, and we simulate the final scale of infection after immunization under the optimal immunization ratio. It can take a minimum of at least 10 years to reduce the spread of this disease, but to eliminate it forever, it needs at least a minimum of 100 years. [ABSTRACT FROM AUTHOR]

The emergence of mutant strains of COVID-19 reduces the effectiveness of vaccines in preventing infection, but remains effective in preventing severe illness and death. This paper established a heterogeneous mixing model of age groups with pharmaceutical and non-pharmaceutical interventions by analyzing the transmission mechanism of breakthrough infection caused by the heterogeneity of protection period under the action of vaccine-preventable infection with the original strain. The control reproduction number R c of the system is analyzed, and the existence and stability of equilibrium are given by the comparison principle. Numerical simulation was conducted to evaluate the vaccination program and intervention measures in the customized scenario, demonstrating that the group-3 coverage rate p 3 plays a key role in R c. It is proposed that accelerating the rate of admission and testing is conducive to epidemic control by further fitting data of COVID-19 transmission in real scenarios. The findings provide a general modeling idea for the emergence of new vaccines to prevent infection by mutant strains, as well as a solid theoretical foundation for mainland China to formulate future vaccination strategies for new vaccines. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics". • A modeling framework of heterogeneous mixing for COVID-19 with NPIs and vaccines. • Breakthrough infection and vaccines to reduce infection were incorporated into model. • Dynamical properties are analyzed, including threshold and stabilities of equilibria. • The vaccination strategies in custom scenario were explored with multiple indicators. [ABSTRACT FROM AUTHOR]

The large-scale infection of COVID-19 has led to a significant impact on lives and economies around the world and has had considerable impact on global public health. Social distancing, mask wearing and contact tracing have contributed to containing or at least mitigating the outbreak, but how public awareness influences the effectiveness and efficiency of such approaches remains unclear. In this study, we developed a discrete compartment dynamic model to mimic and explore how media reporting and the strengthening containment strategies can help curb the spread of COVID-19 using Shaanxi Province, China, as a case study. The targeted model is parameterized based on multi-source data, including the cumulative number of confirmed cases, recovered individuals, the daily number of media-reporting items and the imported cases from the rest of China outside Shaanxi from January 23 to April 11, 2020. We carried out a sensitivity analysis to investigate the effect of media reporting and imported cases on transmission. The results revealed that reducing the intensity of media reporting, which would result in a significant increasing of the contact rate and a sizable decreasing of the contact-tracing rate, could aggravate the outbreak severity by increasing the cumulative number of confirmed cases. It also demonstrated that diminishing the imported cases could alleviate the outbreak severity by reducing the length of the epidemic and the final size of the confirmed cases; conversely, delaying implementation of lockdown strategies could prolong the length of the epidemic and magnify the final size. These findings suggest that strengthening media coverage and timely implementing of lockdown measures can significantly reduce infection.

Background: In December 2019, an outbreak of coronavirus disease (later named as COVID-19) was identified in Wuhan, China and, later on, detected in other parts of China. Our aim is to evaluate the effectiveness of the evolution of interventions and self-protection measures, estimate the risk of partial lifting control measures and predict the epidemic trend of the virus in the mainland of China excluding Hubei province based on the published data and a novel mathematical model. Methods: A novel COVID-19 transmission dynamic model incorporating the intervention measures implemented in China is proposed. COVID-19 daily data of the mainland of China excluding Hubei province, including the cumulative confirmed cases, the cumulative deaths, newly confirmed cases and the cumulative recovered cases between 20 January and 3 March 2020, were archived from the National Health Commission of China (NHCC). We parameterize the model by using the Markov Chain Monte Carlo (MCMC) method and estimate the control reproduction number (Rc), as well as the effective daily reproduction ratio- Re(t), of the disease transmission in the mainland of China excluding Hubei province. Results: The estimation outcomes indicate that Rc is 3.36 (95% CI: 3.20–3.64) and Re(t) has dropped below 1 since 31 January 2020, which implies that the containment strategies implemented by the Chinese government in the mainland of China are indeed effective and magnificently suppressed COVID-19 transmission. Moreover, our results show that relieving personal protection too early may lead to a prolonged disease transmission period and more people would be infected, and may even cause a second wave of epidemic or outbreaks. By calculating the effective reproduction ratio, we prove that the contact rate should be kept at least less than 30% of the normal level by April, 2020. Conclusions: To ensure the pandemic ending rapidly, it is necessary to maintain the current integrated restrict interventions and self-protection measures, including travel restriction, quarantine of entry, contact tracing followed by quarantine and isolation and reduction of contact, like wearing masks, keeping social distance, etc. People should be fully aware of the real-time epidemic situation and keep sufficient personal protection until April. If all the above conditions are met, the outbreak is expected to be ended by April in the mainland of China apart from Hubei province. [ABSTRACT FROM AUTHOR]