Stability analysis and optimal control on a multi-strain coinfection model with amplification and vaccination

In this paper, a multi-strain coinfection model with amplification (or mutation) is established to characterize the interaction between common strain and amplified strain, as well as vaccination. The basic reproduction number ℛ0 is derived, from which the criteria on the existence and local (or global) stability of equilibria (including disease-free, dominant-strain and coexistence-strain) are established. By analyzing the effectiveness of vaccination, we find that a critical inoculation level could make the disease eliminate when ℛ0<1, while inefficient vaccines could cause backward bifurcation when ℛ0<1. Based on sensitivity analysis and realistic control policy, the optimal strategy of disease control is obtained. The theoretical results are illustrated by numerical simulation and clinical data of COVID-19 in Morocco.

Case clustering, contact stratification, and transmission heterogeneity of SARS-CoV-2 Omicron BA.5 variants in Urumqi, China: An observational study.

Background: From August to September 2022, Urumqi, the capital of the Xinjiang Uygur Autonomous Region in China, faced its largest COVID-19 outbreak caused by the emergence of the SARS-CoV-2 Omicron BA.5.2 variants. Although the superspreading of COVID-19 played an important role in triggering large-scale outbreaks, little was known about the superspreading potential and heterogeneity in the transmission of Omicron BA.5 variants. Methods: In this retrospective observational, contact tracing study, we identified 1139 laboratory-confirmed COVID-19 cases of Omicron BA.5.2 variants, and 51 323 test-negative close contacts in Urumqi from 7 August to 7 September 2022. By using detailed contact tracing information and exposure history of linked case-contact pairs, we described stratification in contact and heterogeneity in transmission across different demographic strata, vaccine statuses, and contact settings. We adopted beta-binomial models to characterise the secondary attack rate (SAR) distribution among close contacts and modelled COVID-19 transmission as a branching process with heterogeneity in transmission governed by negative binomial models. Results: After the city lockdown, the mean case cluster size decreased from 2.0 (before lockdown) to 1.6, with decreased proportions of contacts in workplace and community settings compared with household settings. We estimated that 14% of the most infectious index cases generated 80% transmission, whereas transmission in the community setting presented the highest heterogeneity, with 5% index cases seeding 80% transmission. Compared with zero, one, and two doses of inactivated vaccine (Sinopharm), index cases with three doses of vaccine had a lower risk of generating secondary cases in terms of the reproduction number. Contacts of female cases, cases with ages 0-17 years, and household settings had relatively higher SAR. Conclusions: In the context of intensive control measures, active case detection, and relatively high vaccine coverage, but with an infection-naive population, our findings suggested high heterogeneity in the contact and transmission risks of Omicron BA.5 variants across different demographic strata, vaccine statuses, and contact settings. Given the rapid evolution of SARS-CoV-2, investigating the distribution of transmission not only helped promote public awareness and preparedness among high-risk groups, but also highlighted the importance of continuously monitoring the transmission characteristics of genetic variants of SARS-CoV-2.

Analysis and simulation of a stochastic COVID-19 model with large-scale nucleic acid detection and isolation measures: A case study of the outbreak in Urumqi, China in August 2022.

In this paper, a stochastic COVID-19 model with large-scale nucleic acid detection and isolation measures is proposed. Firstly, the existence and uniqueness of the global positive solution is obtained. Secondly, threshold criteria for the stochastic extinction and persistence in the mean with probability one are established. Moreover, a sufficient condition for the existence of unique ergodic stationary distribution for any positive solution is also established. Finally, numerical simulations are carried out in combination with real COVID-19 data from Urumqi, China and the theoretical results are verified.

Patch model for border reopening and control to prevent new outbreaks of COVID-19.

In this paper, we propose a two-patch model with border control to investigate the effect of border control measures and local non-pharmacological interventions (NPIs) on the transmission of COVID-19. The basic reproduction number of the model is calculated, and the existence and stability of the boundary equilibria and the existence of the coexistence equilibrium of the model are obtained. Through numerical simulation, when there are no unquarantined virus carriers in the patch-2, it can be concluded that the reopening of the border with strict border control measures to allow people in patch-1 to move into patch-2 will not lead to disease outbreaks. Also, when there are unquarantined virus carriers in patch-2 (or lax border control causes people carrying the virus to flow into patch-2), the border control is more strict, and the slower the growth of number of new infectious in patch-2, but the strength of border control does not affect the final state of the disease, which is still dependent on local NPIs. Finally, when the border reopens during an outbreak of disease in patch-2, then a second outbreak will happen.

The Effects of Migration and Limited Medical Resources of the Transmission of SARS-CoV-2 Model with Two Patches.

The sudden outbreak of SARS-CoV-2 has caused the shortage of medical resources around the world, especially in developing countries and underdeveloped regions. With the continuous increase in the duration of this disease, the control of migration of humans between regions or countries has to be relaxed. Based on this, we propose a two-patches mathematical model to simulate the transmission of SARS-CoV-2 among two-patches, asymptomatic infected humans and symptomatic infected humans, where a half-saturated detection rate function is also introduced to describe the effect of medical resources. By applying the methods of linearization and constructing a suitable Lyapunov function, the local and global stability of the disease-free equilibrium of this model without migration is obtained. Further, the existence of forward/backward bifurcation is analyzed, which is caused by the limited medical resources. This means that the elimination or prevalence of the disease no longer depends on the basic reproduction number but is closely related to the initial state of asymptomatic and symptomatic infected humans and the supply of medical resources. Finally, the global dynamics of the full model are discussed, and some numerical simulations are carried to explain the main results and the effects of migration and supply of medical resources on the transmission of disease.

Evaluation and prediction of the COVID-19 variations at different input population and quarantine strategies, a case study in Guangdong Province, China

In this study, an epidemic model was developed to simulate and predict the disease variations of Guangdong province which was focused on the period from Jan 27 to Feb 20, 2020. To explore the impacts of the input population and quarantine strategies on the disease variations at different scenarios, four time points were assumed as Feb 6, Feb 16, Feb 24 and Mar 5 2020. The major results suggest that our model can well capture the disease variations with high accuracy. The simulated peak value of the confirmed cases is 1002 at Feb 10, 2020 which is mostly close to the reported number of 1007 at Feb 9, 2020. The disease will become extinction with peak value of 1397 at May 11, 2020. Moreover, the increased numbers of the input population can mainly shorten the disease extinction days and the increased percentages of the exposed individuals of the input population increase the number of cumulative confirmed cases at a small percentage. Increasing the input population and decreasing the quarantine strategy together around the time point of the peak value of the confirmed cases, may lead to the second outbreak.

Dynamical Variations of the Global COVID-19 Pandemic Based on a SEICR Disease Model: A New Approach of Yi Hua Jie Mu.

The ongoing coronavirus disease 2019 (COVID-19) pandemic has caused more than 150 million cases of infection to date and poses a serious threat to global public health. In this study, global COVID-19 data were used to examine the dynamical variations from the perspectives of immunity and contact of 84 countries across the five climate regions: tropical, arid, temperate, and cold. A new approach named Yi Hua Jie Mu is proposed to obtain the transmission rates based on the COVID-19 data between the countries with the same climate region over the Northern Hemisphere and Southern Hemisphere. Our results suggest that the COVID-19 pandemic will persist over a long period of time or enter into regular circulation in multiple periods of 1-2 years. Moreover, based on the simulated results by the COVID-19 data, it is found that the temperate and cold climate regions have higher infection rates than the tropical and arid climate regions, which indicates that climate may modulate the transmission of COVID-19. The role of the climate on the COVID-19 variations should be concluded with more data and more cautions. The non-pharmaceutical interventions still play the key role in controlling and prevention this global pandemic.

Fangcang shelter hospitals during the COVID-19 epidemic, Wuhan, China.

OBJECTIVE: To design models of the spread of coronavirus disease-2019 (COVID-19) in Wuhan and the effect of Fangcang shelter hospitals (rapidly-built temporary hospitals) on the control of the epidemic. METHODS: We used data on daily reported confirmed cases of COVID-19, recovered cases and deaths from the official website of the Wuhan Municipal Health Commission to build compartmental models for three phases of the COVID-19 epidemic. We incorporated the hospital-bed capacity of both designated and Fangcang shelter hospitals. We used the models to assess the success of the strategy adopted in Wuhan to control the COVID-19 epidemic. FINDINGS: Based on the 13 348 Fangcang shelter hospitals beds used in practice, our models show that if the Fangcang shelter hospitals had been opened on 6 February (a day after their actual opening), the total number of COVID-19 cases would have reached 7 413 798 (instead of 50 844) with 1 396 017 deaths (instead of 5003), and the epidemic would have lasted for 179 days (instead of 71). CONCLUSION: While the designated hospitals saved lives of patients with severe COVID-19, it was the increased hospital-bed capacity of the large number of Fangcang shelter hospitals that helped slow and eventually stop the COVID-19 epidemic in Wuhan. Given the current global pandemic of COVID-19, our study suggests that increasing hospital-bed capacity, especially through temporary hospitals such as Fangcang shelter hospitals, to isolate groups of people with mild symptoms within an affected region could help curb and eventually stop COVID-19 outbreaks in communities where effective household isolation is not possible.

2019-nCoV Transmission in Hubei Province, China: Stochastic and Deterministic Analyses

Currently, a novel coronavirus (2019-nCoV) causes an outbreak of viral pneumonia in Hubei province, China. In this paper, stochastic and deterministic models are proposed to investigate the transmission mechanism of 2019-nCoV from 15 January to 5 February 2020 in Hubei province. For the deterministic model, basic reproduction number R-0 is defined and endemic equilibrium is given. Under R-0>1, quasi-stationary distribution of the stochastic process is approximated by Gaussian diffusion. Residual, sensitivity, dynamical, and diffusion analyses of the models are conducted. Further, control variables are introduced to the deterministic model and optimal strategies are provided. Based on empirical results, we suggest that the first and most important thing is to control input, screening, treatment, and isolation.

Dynamic variations of the COVID-19 disease at different quarantine strategies in Wuhan and mainland China.

BACKGROUND: The Coronavirus Disease 2019 (COVID-19) firstly announced in Wuhan of Hubei province, China is rapidly spreading to all the other 31 provinces of China and to more than 140 countries. Quarantine strategies play the key role on the disease controlling and public health in the world with this pandemic of the COVID-19 defined by the World Health Organization. METHODS: In this study, a SEIRQ epidemic model was developed to explore the dynamic changes of COVID-19 in Wuhan and mainland China, from January 27, 2020 to March 5, 2020. Moreover, to investigate the effects of the quarantine strategies, two perspectives are employed from the different quarantine magnitudes and quarantine time points. RESULTS: The major results suggest that the COVID-19 variations are well captured by the epidemic model with very high accuracy in the cumulative confirmed cases, confirmed cases, cumulative recovered cases and cumulative death cases. The quarantine magnitudes in the susceptible individuals play larger roles on the disease control than the impacts of the quarantines of the exposed individuals and infectious individuals. For the quarantine time points, it shows that the early quarantine strategy is significantly important for the disease controlling. The time delayed quarantining will seriously increase the COVID-19 disease patients and prolongs the days of the disease extinction. CONCLUSIONS: Our model can simulate and predict the COVID-19 variations and the quarantine strategies are important for the disease controlling, especially at the early period of the disease outbreak. These conclusions provide important scientific information for the government policymaker in the disease control strategies.