scholarly journals Changing transmission dynamics of COVID-19 in China: a nationwide population-based piecewise mathematical modelling study

2020 ◽  
Author(s):  
Jiawen Hou ◽  
Jie Hong ◽  
Boyun Ji ◽  
Bowen Dong ◽  
Yue Chen ◽  
...  
Keyword(s):  
Mathematical Modelling ◽  
Reproduction Number ◽  
Mainland China ◽  
Hubei Province ◽  
Transmission Dynamics ◽  
Population Movement ◽  
Long Distance ◽  
Spring Festival ◽  
Travel Restrictions ◽  
Controlled Reproduction

AbstractBackgroundThe first case of COVID-19 atypical pneumonia was reported in Wuhan, China on December 1, 2019. Since then, at least 33 other countries have been affected and there is a possibility of a global outbreak. A tremendous amount of effort has been made to understand its transmission dynamics; however, the temporal and spatial transmission heterogeneity and changing epidemiology have been mostly ignored. The epidemic mechanism of COVID-19 remains largely unclear.MethodsEpidemiological data on COVID-19 in China and daily population movement data from Wuhan to other cities were obtained and analyzed. To describe the transmission dynamics of COVID-19 at different spatio-temporal scales, we used a three-stage continuous-time Susceptible-Exposed-Infectious-Recovered (SEIR) meta-population model based on the characteristics and transmission dynamics of each stage: 1) local epidemic from December 1, 2019 to January 9, 2020; 2) long-distance spread due to the Spring Festival travel rush from January 10 to 22, 2020; and 3) intra-provincial transmission from January 23, 2020 when travel restrictions were imposed. Together with the basic reproduction number (R0) for mathematical modelling, we also considered the variation in infectivity and introduced the controlled reproduction number (Rc) by assuming that exposed individuals to be infectious; we then simulated the future spread of COVID across Wuhan and all the provinces in mainland China. In addition, we built a novel source tracing algorithm to infer the initial exposed number of individuals in Wuhan on January 10, 2020, to estimate the number of infections early during this epidemic.FindingsThe spatial patterns of disease spread were heterogeneous. The estimated controlled reproduction number (Rc) in the neighboring provinces of Hubei province were relatively large, and the nationwide reproduction number ‐ except for Hubei ‐ ranged from 0.98 to 2.74 with an average of 1.79 (95% CI 1.77‐1.80). Infectivity was significantly greater for exposed than infectious individuals, and exposed individuals were predicted to have become the major source of infection after January 23. For the epidemic process, most provinces reached their epidemic peak before February 10, 2020. It is expected that the maximum number of infections will be approached by the end of March. The final infectious size is estimated to be about 58,000 for Wuhan, 20,800 for the rest of Hubei province, and 17,000 for the other provinces in mainland China. Moreover, the estimated number of the exposed individuals is much greater than the officially reported number of infectious individuals in Wuhan on January 10, 2020.InterpretationThe transmission dynamics of COVID-19 have been changing over time and were heterogeneous across regions. There was a substantial underestimation of the number of exposed individuals in Wuhan early in the epidemic, and the Spring Festival travel rush played an important role in enhancing and accelerating the spread of COVID-19. However, China’s unprecedented large-scale travel restrictions quickly reduced Rc. The next challenge for the control of COVID-19 will be the second great population movement brought by removing these travel restrictions.

scholarly journals The impact of traffic isolation in Wuhan on the spread of 2019-nCov

2020 ◽  
Author(s):  
Gehui Jin ◽  
Jiayu Yu ◽  
Liyuan Han ◽  
Shiwei Duan
Keyword(s):  
Mortality Rate ◽  
Chinese Spring ◽  
Mainland China ◽  
Hubei Province ◽  
Migrant Population ◽  
Migration Index ◽  
Spring Festival ◽  
The Impact

The 2019-nCoV outbreak occurred near the Chinese Spring Festival transport period in Wuhan. As an important transportation center, the migration of Wuhan accelerated the spread of 2019-nCoV across mainland China. Based on the cumulative Baidu migration index (CBMI), we first analyzed the proportion of Wuhan’s migrant population to other cities. Our results confirm that there is a significant correlation between the export population of Wuhan and reported cases in various regions. We subsequently found that the mortality rate in Hubei Province was much higher than that in other regions of mainland China, while the investigation of potential cases in Wuhan was far behind other provinces in Mainland China, which indicates the effectiveness of early isolation.

scholarly journals Mathematical modelling of pneumonia dynamics of children under the age of five

2021 ◽  
Author(s):  
Idowu Kabir Oluwatobi ◽  
Erinle-Ibrahim L.M
Keyword(s):  
Mathematical Modelling ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Control Measures ◽  
Transmission Dynamics ◽  
Natural Immunity ◽  
Paper Work ◽  
Effect Of Treatment ◽  
The Stability ◽  
Disease Free

Abstract This paper work was designed to study the effect of treatment on the transmission of pneumonia infection. When studying the transmission dynamics of infectious diseases with an objective of suggesting control measures, it is important to consider the stability of equilibrium points. In this paper, basic reproduction number, effective reproduction number, existences and stability of the equilibrium point were established.Using Lyaponov function we discovered that the disease free equilibrium is unstable. The results are presented in graphs and it is discovered that the spread of the infection will be greatly affected by the rate of treatment and natural immunity.

scholarly journals The importance of the timing of quarantine measures before symptom onset to prevent COVID-19 outbreaks - illustrated by Hong Kong’s intervention model

2020 ◽  
Author(s):  
Hsiang-Yu Yuan ◽  
Guiyuan Han ◽  
Hsiangkuo Yuan ◽  
Susanne Pfeiffer ◽  
Axiu Mao ◽  
...  
Keyword(s):  
Hong Kong ◽  
Symptom Onset ◽  
Reproduction Number ◽  
Model Fitting ◽  
Mainland China ◽  
Control Measures ◽  
Rapid Expansion ◽  
Transmission Dynamics ◽  
Population Immunity ◽  
Key Factor

AbstractBackgroundThe rapid expansion of the current COVID-19 outbreak has caused a global pandemic but how quarantine-based measures can prevent or suppress an outbreak without other more intrusive interventions has not yet been determined. Hong Kong had a massive influx of travellers from mainland China, where the outbreak began, during the early expansion period coinciding with the Lunar New Year festival; however, the spread of the virus has been relatively limited even without imposing severe control measures, such as a full city lockdown. Understanding how quarantine measures in Hong Kong were effective in limiting community spread can provide us with valuable insights into how to suppress an outbreak. However, challenges exist in evaluating the effects of quarantine on COVID-19 transmission dynamics in Hong Kong due to the fact that the effects of border control have to be also taken into account.MethodsWe have developed a two-layered susceptible-exposed-infectious-quarantined-recovered (SEIQR) meta-population model which can estimate the effects of quarantine on virus transmissibility after stratifying infections into imported and subsequent community infections, in a region closely connected to the outbreak’s source. We fitted the model to both imported and local confirmed case data with symptom onset from 18 January to 29 February 2020 in Hong Kong, together with daily transportation data and the transmission dynamics of COVID-19 from Wuhan and mainland China. After model fitting, epidemiological parameters and the timing of the start of quarantine for infected cases were estimated.ResultsThe model estimated that the reproduction number of COVID-19 in Hong Kong was 0.76 (95% CI, 0.66 to 0.86), achieved through quarantining infected cases −0.57 days (95% CI, −4.21 − 3.88) relative to symptom onset, with an estimated incubation time of 5.43 days (95% CI, 1.30 − 9.47). However, if delaying the quarantine start by more than 1.43 days, the reproduction number would be greater than one, making community spread more likely. The model also determined the timing of the start of quarantine necessary in order to suppress an outbreak in the presence of population immunity.ConclusionThe results suggest that the early quarantine for infected cases before symptom onset is a key factor to prevent COVID-19 outbreak.

scholarly journals Outbreak of COVID-19 and SARS in mainland China: a comparative study based on national surveillance data

BMJ Open ◽  
2020 ◽  
Vol 10 (10) ◽  
pp. e043411
Author(s):  
Lin Zhao ◽  
Dan Feng ◽  
Run-Ze Ye ◽  
Hai-Tao Wang ◽  
Yu-Hao Zhou ◽  
...  
Keyword(s):  
Comparative Study ◽  
Reproduction Number ◽  
Mainland China ◽  
Case Fatality ◽  
Control Measures ◽  
Transmission Dynamics ◽  
Onset Date ◽  
Data Set ◽  
Illness Onset ◽  
Epidemiological Characteristics

ObjectiveTo compare the epidemiological characteristics and transmission dynamics in relation to interventions against the COVID-19 and severe acute respiratory syndrome (SARS) outbreak in mainland China.DesignComparative study based on a unique data set of COVID-19 and SARS.SettingOutbreak in mainland China.ParticipantsThe final database included 82 858 confirmed cases of COVID-19 and 5327 cases of SARS.MethodsWe brought together all existing data sources and integrated them into a comprehensive data set. Individual information on age, sex, occupation, residence location, date of illness onset, date of diagnosis and clinical outcome was extracted. Control measures deployed in mainland China were collected. We compared the epidemiological and spatial characteristics of COVID-19 and SARS. We estimated the effective reproduction number to explore differences in transmission dynamics and intervention effects.ResultsCompared with SARS, COVID-19 affected more extensive areas (1668 vs 230 counties) within a shorter time (101 vs 193 days) and had higher attack rate (61.8 vs 4.0 per million persons). The COVID-19 outbreak had only one epidemic peak and one epicentre (Hubei Province), while the SARS outbreak resulted in two peaks and two epicentres (Guangdong Province and Beijing). SARS-CoV-2 was more likely to infect older people (median age of 52 years), while SARS-CoV tended to infect young adults (median age of 34 years). The case fatality rate (CFR) of either disease increased with age, but the CFR of COVID-19 was significantly lower than that of SARS (5.6% vs 6.4%). The trajectory of effective reproduction number dynamically changed in relation to interventions, which fell below 1 within 2 months for COVID-19 and within 5.5 months for SARS.ConclusionsChina has taken more prompt and effective responses to combat COVID-19 by learning lessons from SARS, providing us with some epidemiological clues to control the ongoing COVID-19 pandemic worldwide.

scholarly journals Development of the reproduction number from coronavirus SARS-CoV-2 case data in Germany and implications for political measures

BMC Medicine ◽  
2021 ◽  
Vol 19 (1) ◽  
Author(s):  
Sahamoddin Khailaie ◽  
Tanmay Mitra ◽  
Arnab Bandyopadhyay ◽  
Marta Schips ◽  
Pietro Mascheroni ◽  
...  
Keyword(s):  
Structural Changes ◽  
Reproduction Number ◽  
National Level ◽  
Transmission Dynamics ◽  
Federal State ◽  
Parameter Estimates ◽  
Time Varying ◽  
Short Term ◽  
Robert Koch Institute ◽  
Federal States

Abstract Background SARS-CoV-2 has induced a worldwide pandemic and subsequent non-pharmaceutical interventions (NPIs) to control the spread of the virus. As in many countries, the SARS-CoV-2 pandemic in Germany has led to a consecutive roll-out of different NPIs. As these NPIs have (largely unknown) adverse effects, targeting them precisely and monitoring their effectiveness are essential. We developed a compartmental infection dynamics model with specific features of SARS-CoV-2 that allows daily estimation of a time-varying reproduction number and published this information openly since the beginning of April 2020. Here, we present the transmission dynamics in Germany over time to understand the effect of NPIs and allow adaptive forecasts of the epidemic progression. Methods We used a data-driven estimation of the evolution of the reproduction number for viral spreading in Germany as well as in all its federal states using our model. Using parameter estimates from literature and, alternatively, with parameters derived from a fit to the initial phase of COVID-19 spread in different regions of Italy, the model was optimized to fit data from the Robert Koch Institute. Results The time-varying reproduction number (Rt) in Germany decreased to <1 in early April 2020, 2–3 weeks after the implementation of NPIs. Partial release of NPIs both nationally and on federal state level correlated with moderate increases in Rt until August 2020. Implications of state-specific Rt on other states and on national level are characterized. Retrospective evaluation of the model shows excellent agreement with the data and usage of inpatient facilities well within the healthcare limit. While short-term predictions may work for a few weeks, long-term projections are complicated by unpredictable structural changes. Conclusions The estimated fraction of immunized population by August 2020 warns of a renewed outbreak upon release of measures. A low detection rate prolongs the delay reaching a low case incidence number upon release, showing the importance of an effective testing-quarantine strategy. We show that real-time monitoring of transmission dynamics is important to evaluate the extent of the outbreak, short-term projections for the burden on the healthcare system, and their response to policy changes.

MODELING THE IMPACT OF VOLUNTARY TESTING AND TREATMENT ON TUBERCULOSIS TRANSMISSION DYNAMICS

2012 ◽  
Vol 05 (04) ◽  
pp. 1250029 ◽  
Author(s):  
S. MUSHAYABASA ◽  
C. P. BHUNU
Keyword(s):  
Deterministic Model ◽  
Reproduction Number ◽  
Positive Impact ◽  
Transmission Dynamics ◽  
Effective Control ◽  
Reproductive Number ◽  
Voluntary Testing ◽  
Manifold Theory ◽  
The Impact ◽  
Disease Free

A deterministic model for evaluating the impact of voluntary testing and treatment on the transmission dynamics of tuberculosis is formulated and analyzed. The epidemiological threshold, known as the reproduction number is derived and qualitatively used to investigate the existence and stability of the associated equilibrium of the model system. The disease-free equilibrium is shown to be locally-asymptotically stable when the reproductive number is less than unity, and unstable if this threshold parameter exceeds unity. It is shown, using the Centre Manifold theory, that the model undergoes the phenomenon of backward bifurcation where the stable disease-free equilibrium co-exists with a stable endemic equilibrium when the associated reproduction number is less than unity. The analysis of the reproduction number suggests that voluntary tuberculosis testing and treatment may lead to effective control of tuberculosis. Furthermore, numerical simulations support the fact that an increase voluntary tuberculosis testing and treatment have a positive impact in controlling the spread of tuberculosis in the community.

scholarly journals Mathematical Analysis of Influenza A Dynamics in the Emergence of Drug Resistance

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Caroline W. Kanyiri ◽  
Kimathi Mark ◽  
Livingstone Luboobi
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Drug Resistance ◽  
Stability Analysis ◽  
Influenza A ◽  
Reproduction Number ◽  
Critical Value ◽  
Backward Bifurcation ◽  
Transmission Dynamics ◽  
High Morbidity

Every year, influenza causes high morbidity and mortality especially among the immunocompromised persons worldwide. The emergence of drug resistance has been a major challenge in curbing the spread of influenza. In this paper, a mathematical model is formulated and used to analyze the transmission dynamics of influenza A virus having incorporated the aspect of drug resistance. The qualitative analysis of the model is given in terms of the control reproduction number,Rc. The model equilibria are computed and stability analysis carried out. The model is found to exhibit backward bifurcation prompting the need to lowerRcto a critical valueRc∗for effective disease control. Sensitivity analysis results reveal that vaccine efficacy is the parameter with the most control over the spread of influenza. Numerical simulations reveal that despite vaccination reducing the reproduction number below unity, influenza still persists in the population. Hence, it is essential, in addition to vaccination, to apply other strategies to curb the spread of influenza.

scholarly journals Transmission dynamics of Monkeypox virus: a mathematical modelling approach

2021 ◽  
Author(s):  
Olumuyiwa James Peter ◽  
Sumit Kumar ◽  
Nitu Kumari ◽  
Festus Abiodun Oguntolu ◽  
Kayode Oshinubi ◽  
...  
Keyword(s):  
Mathematical Modelling ◽  
Transmission Dynamics ◽  
Monkeypox Virus ◽  
Modelling Approach

scholarly journals Evolving epidemiology of novel coronavirus diseases 2019 and possible interruption of local transmission outside Hubei Province in China: a descriptive and modeling study

2020 ◽  
Author(s):  
Juanjuan Zhang ◽  
Maria Litvinova ◽  
Wei Wang ◽  
Yan Wang ◽  
Xiaowei Deng ◽  
...  
Keyword(s):  
Age Groups ◽  
Mainland China ◽  
The Elderly ◽  
Hubei Province ◽  
Epidemic Threshold ◽  
Epidemic Dynamics ◽  
Serial Interval ◽  
The Mean ◽  
Novel Coronavirus ◽  
Local Transmission

AbstractBackgroundThe COVID-19 epidemic originated in Wuhan City of Hubei Province in December 2019 and has spread throughout China. Understanding the fast evolving epidemiology and transmission dynamics of the outbreak beyond Hubei would provide timely information to guide intervention policy.MethodsWe collected individual information on 8,579 laboratory-confirmed cases from official publically sources reported outside Hubei in mainland China, as of February 17, 2020. We estimated the temporal variation of the demographic characteristics of cases and key time-to-event intervals. We used a Bayesian approach to estimate the dynamics of the net reproduction number (Rt) at the provincial level.ResultsThe median age of the cases was 44 years, with an increasing of cases in younger age groups and the elderly as the epidemic progressed. The delay from symptom onset to hospital admission decreased from 4.4 days (95%CI: 0.0-14.0) until January 27 to 2.6 days (0.0-9.0) from January 28 to February 17. The mean incubation period was estimated at 5.2 days (1.8-12.4) and the mean serial interval at 5.1 days (1.3-11.6). The epidemic dynamics in provinces outside Hubei was highly variable, but consistently included a mix of case importations and local transmission. We estimate that the epidemic was self-sustained for less than three weeks with Rt reaching peaks between 1.40 (1.04-1.85) in Shenzhen City of Guangdong Province and 2.17 (1.69-2.76) in Shandong Province. In all the analyzed locations (n=10) Rt was estimated to be below the epidemic threshold since the end of January.ConclusionOur findings suggest that the strict containment measures and movement restrictions in place may contribute to the interruption of local COVID-19 transmission outside Hubei Province. The shorter serial interval estimated here implies that transmissibility is not as high as initial estimates suggested.

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