Unravelling the dynamics of the COVID-19 pandemic with the effect of vaccination, vertical transmission and hospitalization.

The coronavirus disease 2019 (COVID-19) is caused by a newly emerged virus known as severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), transmitted through air droplets from an infected person. However, other transmission routes are reported, such as vertical transmission. Here, we propose an epidemic model that considers the combined effect of vertical transmission, vaccination and hospitalization to investigate the dynamics of the virus's dissemination. Rigorous mathematical analysis of the model reveals that two equilibria exist: the disease-free equilibrium, which is locally asymptotically stable when the basic reproduction number ( R 0 ) is less than 1 (unstable otherwise), and an endemic equilibrium, which is globally asymptotically stable when R 0 > 1 under certain conditions, implying the plausibility of the disease to spread and cause large outbreaks in a community. Moreover, we fit the model using the Saudi Arabia cases scenario, which designates the incidence cases from the in-depth surveillance data as well as displays the epidemic trends in Saudi Arabia. Through Caputo fractional-order, simulation results are provided to show dynamics behaviour on the model parameters. Together with the non-integer order variant, the proposed model is considered to explain various dynamics features of the disease. Further numerical simulations are carried out using an efficient numerical technique to offer additional insight into the model's dynamics and investigate the combined effect of vaccination, vertical transmission, and hospitalization. In addition, a sensitivity analysis is conducted on the model parameters against the R 0 and infection attack rate to pinpoint the most crucial parameters that should be emphasized in controlling the pandemic effectively. Finally, the findings suggest that adequate vaccination coupled with basic non-pharmaceutical interventions are crucial in mitigating disease incidences and deaths.

Characterizing superspreading potential of infectious disease: Decomposition of individual transmissibility.

In the context of infectious disease transmission, high heterogeneity in individual infectiousness indicates that a few index cases can generate large numbers of secondary cases, a phenomenon commonly known as superspreading. The potential of disease superspreading can be characterized by describing the distribution of secondary cases (of each seed case) as a negative binomial (NB) distribution with the dispersion parameter, k. Based on the feature of NB distribution, there must be a proportion of individuals with individual reproduction number of almost 0, which appears restricted and unrealistic. To overcome this limitation, we generalized the compound structure of a Poisson rate and included an additional parameter, and divided the reproduction number into independent and additive fixed and variable components. Then, the secondary cases followed a Delaporte distribution. We demonstrated that the Delaporte distribution was important for understanding the characteristics of disease transmission, which generated new insights distinct from the NB model. By using real-world dataset, the Delaporte distribution provides improvements in describing the distributions of COVID-19 and SARS cases compared to the NB distribution. The model selection yielded increasing statistical power with larger sample sizes as well as conservative type I error in detecting the improvement in fitting with the likelihood ratio (LR) test. Numerical simulation revealed that the control strategy-making process may benefit from monitoring the transmission characteristics under the Delaporte framework. Our findings highlighted that for the COVID-19 pandemic, population-wide interventions may control disease transmission on a general scale before recommending the high-risk-specific control strategies.

Transmission dynamics of COVID-19 pandemic with combined effects of relapse, reinfection and environmental contribution: A modeling analysis.

Reinfection and reactivation of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) have recently raised public health pressing concerns in the fight against the current pandemic globally. In this study, we propose a new dynamic model to study the transmission of the coronavirus disease 2019 (COVID-19) pandemic. The model incorporates possible relapse, reinfection and environmental contribution to assess the combined effects on the overall transmission dynamics of SARS-CoV-2. The model's local asymptotic stability is analyzed qualitatively. We derive the formula for the basic reproduction number ( R 0 ) and final size epidemic relation, which are vital epidemiological quantities that are used to reveal disease transmission status and guide control strategies. Furthermore, the model is validated using the COVID-19 reported situations in Saudi Arabia. Moreover, sensitivity analysis is examined by implementing a partial rank correlation coefficient technique to obtain the ultimate rank model parameters to control or mitigate the pandemic effectively. Finally, we employ a standard Euler technique for numerical simulations of the model to elucidate the influence of some crucial parameters on the overall transmission dynamics. Our results highlight that contact rate, hospitalization rate, and reactivation rate are the fundamental parameters that need particular emphasis for the prevention, mitigation and control.

The non-pharmaceutical interventions may affect the advantage in transmission of mutated variants during epidemics: A conceptual model for COVID-19.

As the COVID-19 pandemic continues, genetic mutations in SARS-CoV-2 emerge, and some of them are found more contagious than the previously identified strains, acting as the major mechanism for many large-scale epidemics. The transmission advantage of mutated variants is widely believed as an innate biological feature that is difficult to be altered by artificial factors. In this study, we explore how non-pharmaceutical interventions (NPI) may affect transmission advantage. A two-strain compartmental epidemic model is proposed and simulated to investigate the biological mechanism of the relationships among different NPIs, the changes in transmissibility of each strain and transmission advantage. Although the NPIs are effective in flattening the epidemic curve, we demonstrate that NPIs probably lead to a decline in transmission advantage, which is likely to occur if the NPIs become intensive. Our findings uncover the mechanistic relationship between NPIs and transmission advantage dynamically, and highlight the important role of NPIs not only in controlling the intensity of epidemics but also in slowing or even containing the growth of the proportion of variants.

Seroprevalence and infection attack rate of COVID-19 in Indian cities.

Objectives: Serological surveys were used to infer the infection attack rate in different populations. The sensitivity of the testing assay, Abbott, drops fast over time since infection which makes the serological data difficult to interpret. In this work, we aim to solve this issue. Methods: We collect longitudinal serological data of Abbott to construct a sensitive decay function. We use the reported COVID-19 deaths to infer the infections, and use the decay function to simulate the seroprevalence and match to the reported seroprevalence in 12 Indian cities. Results: Our model simulated seroprevalence matchs the reported seroprevalence in most of the 12 Indian cities. We obtain reasonable infection attack rate and infection fatality rate for most of the 12 Indian cities. Conclusions: Using both reported COVID-19 deaths data and serological survey data, we infer the infection attack rate and infection fatality rate with increased confidence.

The non-pharmaceutical interventions may affect the advantage in transmission of mutated variants during epidemics: A conceptual model for COVID-19

As the COVID-19 pandemic continues, genetic mutations in SARS-CoV-2 emerge, and some of them are found more contagious than the previously identified strains, acting as the major mechanism for many large-scale epidemics. The transmission advantage of mutated variants is widely believed as an innate biological feature that cannot be altered by artificial factors. In this study, we explore how non-pharmaceutical interventions (NPI) may affect transmission advantage. A two-strain compartmental epidemic model is proposed and simulated to investigate the biological mechanism of the relationships among different NPIs, the changes in transmissibility of each strain and transmission advantage. Although the NPIs are effective in flattening the epidemic curve, we demonstrate that NPIs probably lead to a decline in transmission advantage, which is likely to occur if the NPIs become intensive. Our findings uncover the mechanistic relationship between NPIs and transmission advantage dynamically, and highlight the important role of NPIs not only in controlling the intensity of epidemics but also in showing or even containing the growth of the proportion of mutated variants.

The co-circulating transmission dynamics of SARS-CoV-2 Alpha and Eta variants in Nigeria: A retrospective modeling study of COVID-19.

BACKGROUND: The COVID-19 pandemic poses serious threats to public health globally, and the emerging mutations in SARS-CoV-2 genomes has become one of the major challenges of disease control. In the second epidemic wave in Nigeria, the roles of co-circulating SARS-CoV-2 Alpha (ie, B.1.1.7) and Eta (ie, B.1.525) variants in contributing to the epidemiological outcomes were of public health concerns for investigation. METHODS: We developed a mathematical model to capture the transmission dynamics of different types of strains in Nigeria. By fitting to the national-wide COVID-19 surveillance data, the transmission advantages of SARS-CoV-2 variants were estimated by likelihood-based inference framework. RESULTS: The reproduction numbers were estimated to decrease steadily from 1.5 to 0.8 in the second epidemic wave. In December 2020, when both Alpha and Eta variants were at low prevalent levels, their transmission advantages (against the wild type) were estimated at 1.51 (95% credible intervals (CrI) = 1.48, 1.54), and 1.56 (95% CrI = 1.54, 1.59), respectively. In January 2021, when the original variants almost vanished, we estimated a weak but significant transmission advantage of Eta against Alpha variants with 1.14 (95% CrI = 1.11, 1.16). CONCLUSIONS: Our findings suggested evidence of the transmission advantages for both Alpha and Eta variants, of which Eta appeared slightly more infectious than Alpha. We highlighted the critical importance of COVID-19 control measures in mitigating the outbreak size and relaxing the burdens to health care systems in Nigeria.

Modelling of Waning of Immunity and Reinfection Induced Antibody Boosting of SARS-CoV-2 in Manaus, Brazil.

It was reported that the Brazilian city, Manaus, likely exceeded the herd immunity threshold (presumably 60-70%) in November 2020 after the first wave of COVID-19, based on the serological data of a routine blood donor. However, a second wave started in November 2020, when an even higher magnitude of deaths hit the city. The arrival of the second wave coincided with the emergence of the Gamma (P.1) variant of SARS-CoV-2, with higher transmissibility, a younger age profile of cases, and a higher hospitalization rate. Prete et al. (2020 MedRxiv 21256644) found that 8 to 33 of 238 (3.4-13.9%) repeated blood donors likely were infected twice in Manaus between March 2020 and March 2021. It is unclear how this finding can be used to explain the second wave. We propose a simple model which allows reinfection to explain the two-wave pattern in Manaus. We find that the two waves with 30% and 40% infection attack rates, respectively, and a reinfection ratio at 3.4-13.9%, can explain the two waves well. We argue that the second wave was likely because the city had not exceeded the herd immunity level after the first wave. The reinfection likely played a weak role in causing the two waves.

Shrinkage in serial intervals across transmission generations of COVID-19.

One of the key epidemiological characteristics that shape the transmission of coronavirus disease 2019 (COVID-19) is the serial interval (SI). Although SI is commonly considered following a probability distribution at a population scale, recent studies reported a slight shrinkage (or contraction) of the mean of effective SI across transmission generations or over time. Here, we develop a likelihood-based statistical inference framework with truncation to explore the change in SI across transmission generations after adjusting the impacts of case isolation. The COVID-19 contact tracing surveillance data in Hong Kong are used for exemplification. We find that for COVID-19, the mean of individual SI is likely to shrink with a factor at 0.72 per generation (95%CI: 0.54, 0.96) as the transmission generation increases, where a threshold may exist as the lower boundary of this shrinking process. We speculate that one of the probable explanations for the shrinkage in SI might be an outcome due to the competition among multiple candidate infectors within the same case cluster. Thus, the nonpharmaceutical interventive strategies are crucially important to block the transmission chains, and mitigate the COVID-19 epidemic.

Vertical Transmission of SARS-CoV-2: A Systematic Review of Systematic Reviews.

The COVID-19 pandemic has hugely impacted global public health and economy. The COVID-19 has also shown potential impacts on maternal perinatal and neonatal outcomes. This systematic review aimed to summarize the evidence from existing systematic reviews about the effects of SARS-CoV-2 infections on maternal perinatal and neonatal outcomes. We searched PubMed, MEDLINE, Embase, and Web of Science in accordance with PRISMA guidelines, from 1 December 2019 to 7 July 2021, for published review studies that included case reports, primary studies, clinical practice guidelines, overviews, case-control studies, and observational studies. Systematic reviews that reported the plausibility of mother-to-child transmission of COVID-19 (also known as vertical transmission), maternal perinatal and neonatal outcomes, and review studies that addressed the effect of SARS-CoV-2 infection during pregnancy were also included. We identified 947 citations, of which 69 studies were included for further analysis. Most (>70%) of the mother-to-child infection was likely due to environmental exposure, although a significant proportion (about 20%) was attributable to potential vertical transmission of SARS-CoV-2. Further results of the review indicated that the mode of delivery of pregnant women infected with SARS-CoV-2 could not increase or decrease the risk of infection for the newborns (outcomes), thereby emphasizing the significance of breastfeeding. The issue of maternal perinatal and neonatal outcomes with SARS-CoV-2 infection continues to worsen during the ongoing COVID-19 pandemic, increasing maternal and neonatal mortality, stillbirth, ruptured ectopic pregnancies, and maternal depression. Based on this study, we observed increasing rates of cesarean delivery from mothers with SARS-CoV-2 infection. We also found that SARS-CoV-2 could be potentially transmitted vertically during the gestation period. However, more data are needed to further investigate and follow-up, especially with reports of newborns infected with SARS-CoV-2, in order to examine a possible long-term adverse effect.

Using Proper Mean Generation Intervals in Modeling of COVID-19.

In susceptible-exposed-infectious-recovered (SEIR) epidemic models, with the exponentially distributed duration of exposed/infectious statuses, the mean generation interval (GI, time lag between infections of a primary case and its secondary case) equals the mean latent period (LP) plus the mean infectious period (IP). It was widely reported that the GI for COVID-19 is as short as 5 days. However, many works in top journals used longer LP or IP with the sum (i.e., GI), e.g., >7 days. This discrepancy will lead to overestimated basic reproductive number and exaggerated expectation of infection attack rate (AR) and control efficacy. We argue that it is important to use suitable epidemiological parameter values for proper estimation/prediction. Furthermore, we propose an epidemic model to assess the transmission dynamics of COVID-19 for Belgium, Israel, and the United Arab Emirates (UAE). We estimated a time-varying reproductive number [R0(t)] based on the COVID-19 deaths data and we found that Belgium has the highest AR followed by Israel and the UAE.

Reinfection or Reactivation of Severe Acute Respiratory Syndrome Coronavirus 2: A Systematic Review.

As the pandemic continues, individuals with re-detectable positive (RP) SARS-CoV-2 viral RNA among recovered COVID-19 patients have raised public health concerns. It is imperative to investigate whether the cases with re-detectable positive (RP) SARS-CoV-2 might cause severe infection to the vulnerable population. In this work, we conducted a systematic review of recent literature to investigate reactivation and reinfection among the discharged COVID-19 patients that are found positive again. Our study, consisting more than a total of 113,715 patients, indicates that the RP-SARS-CoV-2 scenario occurs plausibly due to reactivation, reinfection, viral shedding, or testing errors. Nonetheless, we observe that previously infected individuals have significantly lower risk of being infected for the second time, indicating that reactivation or reinfection of SARS-CoV-2 likely have relatively less impact in the general population than the primary infection.

Estimating the generation interval and inferring the latent period of COVID-19 from the contact tracing data.

The coronavirus disease 2019 (COVID-19) emerged by end of 2019, and became a serious public health threat globally in less than half a year. The generation interval and latent period, though both are of importance in understanding the features of COVID-19 transmission, are difficult to observe, and thus they can rarely be learnt from surveillance data empirically. In this study, we develop a likelihood framework to estimate the generation interval and incubation period simultaneously by using the contact tracing data of COVID-19 cases, and infer the pre-symptomatic transmission proportion and latent period thereafter. We estimate the mean of incubation period at 6.8 days (95 %CI: 6.2, 7.5) and SD at 4.1 days (95 %CI: 3.7, 4.8), and the mean of generation interval at 6.7 days (95 %CI: 5.4, 7.6) and SD at 1.8 days (95 %CI: 0.3, 3.8). The basic reproduction number is estimated ranging from 1.9 to 3.6, and there are 49.8 % (95 %CI: 33.3, 71.5) of the secondary COVID-19 infections likely due to pre-symptomatic transmission. Using the best estimates of model parameters, we further infer the mean latent period at 3.3 days (95 %CI: 0.2, 7.9). Our findings highlight the importance of both isolation for symptomatic cases, and for the pre-symptomatic and asymptomatic cases.

High Infection Fatality Rate Among Elderly and Risk Factors Associated With Infection Fatality Rate and Asymptomatic Infections of COVID-19 Cases in Hong Kong.

Background: Since the emergence in December 2019, the COVID-19 pandemic has become one of the greatest global public health threats in history. However, asymptomatic infections have increased the challenges of providing accurate estimates for the infection fatality rate (IFR) of COVID-19. Methods: We calculated the asymptomatic case ratios based on the reported COVID-19 cases in Hong Kong where intensive testing has been conducted in close contacts and high-risk populations. We estimated the IFR using both symptomatic and asymptomatic cases as denominator. The boosted regression tree (BRT) and multivariable logistic regression models were used to identify relative contribution and effect size of the risk factors associated with the asymptomatic cases and IFRs. Results: The ratio of the asymptomatic patients in Hong Kong was higher than many other regions over the world. Imported cases had a higher asymptomatic proportion than local cases. Older age and male were associated with a higher IFR than younger age and females. Conclusion: Policymakers should consider the potential risk factors for the asymptomatic infections and IFRs by the Hong Kong surveillance data to mitigate the diseases and reduce the case mortality of COVID-19.

Transmission dynamics of SARS-CoV-2: A modeling analysis with high-and-moderate risk populations.

Nigeria is second to South Africa with the highest reported cases of COVID-19 in sub-Saharan Africa. In this paper, we employ an SEIR-based compartmental model to study and analyze the transmission dynamics of SARS-CoV-2 outbreaks in Nigeria. The model incorporates different group of populations (that is, high- and- moderate risk populations) and is use to investigate the influence on each population on the overall transmission dynamics.The model, which is fitted well to the data, is qualitatively analyzed to evaluate the impacts of different schemes for controlstrategies. Mathematical analysis reveals that the model has two equilibria; i.e., disease-free equilibrium (DFE) which is local asymptotic stability (LAS) if the basic reproduction number ( R 0 ) is less than 1; and unstable for R 0 > 1 , and an endemic equilibrium (EE) which is globally asymptotic stability (LAS) whenever R 0 > 1 . Furthermore, we find that the model undergoes a phenomenon of backward bifurcation (BB, a coexistence of stable DFE and stable EE even if the R 0 < 1 ). We employ Partial Rank Correlation coefficients (PRCCs) for sensitivity analyses to evaluate the model's parameters. Our results highlight that proper surveillance, especially movement of individuals from high risk to moderate risk population, testing, as well as imposition of other NPIs measures are vital strategies for mitigating the COVID-19 epidemic in Nigeria. Besides, in the absence of an exact solution for the proposed model, we solve the model with the well-known ODE45 numerical solver and the effective numerical schemes such as Euler (EM), Runge-Kutta of order 2 (RK-2), and Runge-Kutta of order 4 (RK-4) in order to establish approximate solutions and to show the physical features of the model. It has been shown that these numerical schemes are very effective and efficient to establish superb approximate solutions for differential equations.

Estimation of COVID-19 under-ascertainment in Kano, Nigeria during the early phase of the epidemics

Estimating the number of cases under-ascertained by inconsistencies is an essential concept in epidemiology. The aim of this study is to estimate the number of COVID-19 under- ascertained (η), and the basic reproduction number (R0) in Kano, Nigeria during the early epidemic period. We adopt a simple exponential growth model to capture the COVID-19 epidemic curve in Kano. Our findings indicate that the early epidemic growth mimics an exponential growth pattern. We find that the number of COVID-19 cases under-ascertained likely occurred during the fourth week of April 2020, and should be considered for future epidemiological investigations and mitigation plan.

Inferencing superspreading potential using zero-truncated negative binomial model: exemplification with COVID-19.

BACKGROUND: In infectious disease transmission dynamics, the high heterogeneity in individual infectiousness indicates that few index cases generate large numbers of secondary cases, which is commonly known as superspreading events. The heterogeneity in transmission can be measured by describing the distribution of the number of secondary cases as a negative binomial (NB) distribution with dispersion parameter, k. However, such inference framework usually neglects the under-ascertainment of sporadic cases, which are those without known epidemiological link and considered as independent clusters of size one, and this may potentially bias the estimates. METHODS: In this study, we adopt a zero-truncated likelihood-based framework to estimate k. We evaluate the estimation performance by using stochastic simulations, and compare it with the baseline non-truncated version. We exemplify the analytical framework with three contact tracing datasets of COVID-19. RESULTS: We demonstrate that the estimation bias exists when the under-ascertainment of index cases with 0 secondary case occurs, and the zero-truncated inference overcomes this problem and yields a less biased estimator of k. We find that the k of COVID-19 is inferred at 0.32 (95%CI: 0.15, 0.64), which appears slightly smaller than many previous estimates. We provide the simulation codes applying the inference framework in this study. CONCLUSIONS: The zero-truncated framework is recommended for less biased transmission heterogeneity estimates. These findings highlight the importance of individual-specific case management strategies to mitigate COVID-19 pandemic by lowering the transmission risks of potential super-spreaders with priority.

Estimation of exponential growth rate and basic reproduction number of the coronavirus disease 2019 (COVID-19) in Africa.

BACKGROUND: Since the first case of coronavirus disease 2019 (COVID-19) in Africa was detected on February 14, 2020, the cumulative confirmations reached 15 207 including 831 deaths by April 13, 2020. Africa has been described as one of the most vulnerable region with the COVID-19 infection during the initial phase of the outbreak, due to the fact that Africa is a great commercial partner of China and some other EU and American countries. Which result in large volume of travels by traders to the region more frequently and causing African countries face even bigger health threat during the COVID-19 pandemic. Furthermore, the fact that the control and management of COVID-19 pandemic rely heavily on a country's health care system, and on average Africa has poor health care system which make it more vulnerable indicating a need for timely intervention to curtail the spread. In this paper, we estimate the exponential growth rate and basic reproduction number (R0) of COVID-19 in Africa to show the potential of the virus to spread, and reveal the importance of sustaining stringent health measures to control the disease in Africa. METHODS: We analyzed the initial phase of the epidemic of COVID-19 in Africa between 1 March and 13 April 2020, by using the simple exponential growth model. We examined the publicly available materials published by the WHO situation report to show the potential of COVID-19 to spread without sustaining strict health measures. The Poisson likelihood framework is adopted for data fitting and parameter estimation. We modelled the distribution of COVID-19 generation interval (GI) as Gamma distributions with a mean of 4.7 days and standard deviation of 2.9 days estimated from previous work, and compute the basic reproduction number. RESULTS: We estimated the exponential growth rate as 0.22 per day (95% CI: 0.20-0.24), and the basic reproduction number, R0, as 2.37 (95% CI: 2.22-2.51) based on the assumption that the exponential growth starting from 1 March 2020. With an R0 at 2.37, we quantified the instantaneous transmissibility of the outbreak by the time-varying effective reproductive number to show the potential of COVID-19 to spread across African region. CONCLUSIONS: The initial growth of COVID-19 cases in Africa was rapid and showed large variations across countries. Our estimates should be useful in preparedness planning against further spread of the COVID-19 epidemic in Africa.

Imitation dynamics in the mitigation of the novel coronavirus disease (COVID-19) outbreak in Wuhan, China from 2019 to 2020.

BACKGROUND: The coronavirus disease 2019 (COVID-19) was first identified in Wuhan, China on December 2019 in patients presenting with atypical pneumonia. Although 'city-lockdown' policy reduced the spatial spreading of the COVID-19, the city-level outbreaks within each city remain a major concern to be addressed. The local or regional level disease control mainly depends on individuals self-administered infection prevention actions. The contradiction between choice of taking infection prevention actions or not makes the elimination difficult under a voluntary acting scheme, and represents a clash between the optimal choice of action for the individual interest and group interests. METHODS: We develop a compartmental epidemic model based on the classic susceptible-exposed-infectious-recovered model and use this to fit the data. Behavioral imitation through a game theoretical decision-making process is incorporated to study and project the dynamics of the COVID-19 outbreak in Wuhan, China. By varying the key model parameters, we explore the probable course of the outbreak in terms of size and timing under several public interventions in improving public awareness and sensitivity to the infection risk as well as their potential impact. RESULTS: We estimate the basic reproduction number, R 0, to be 2.5 (95% CI: 2.4-2.7). Under the current most realistic setting, we estimate the peak size at 0.28 (95% CI: 0.24-0.32) infections per 1,000 population. In Wuhan, the final size of the outbreak is likely to infect 1.35% (95% CI: 1.00-2.12%) of the population. The outbreak will be most likely to peak in the first half of February and drop to daily incidences lower than 10 in June 2020. Increasing sensitivity to take infection prevention actions and the effectiveness of infection prevention measures are likely to mitigate the COVID-19 outbreak in Wuhan. CONCLUSIONS: Through an imitating social learning process, individual-level behavioral change on taking infection prevention actions have the potentials to significantly reduce the COVID-19 outbreak in terms of size and timing at city-level. Timely and substantially resources and supports for improving the willingness-to-act and conducts of self-administered infection prevention actions are recommended to reduce to the COVID-19 associated risks.

A conceptual model for the coronavirus disease 2019 (COVID-19) outbreak in Wuhan, China with individual reaction and governmental action.

The ongoing coronavirus disease 2019 (COVID-19) outbreak, emerged in Wuhan, China in the end of 2019, has claimed more than 2600 lives as of 24 February 2020 and posed a huge threat to global public health. The Chinese government has implemented control measures including setting up special hospitals and travel restriction to mitigate the spread. We propose conceptual models for the COVID-19 outbreak in Wuhan with the consideration of individual behavioural reaction and governmental actions, e.g., holiday extension, travel restriction, hospitalisation and quarantine. We employe the estimates of these two key components from the 1918 influenza pandemic in London, United Kingdom, incorporated zoonotic introductions and the emigration, and then compute future trends and the reporting ratio. The model is concise in structure, and it successfully captures the course of the COVID-19 outbreak, and thus sheds light on understanding the trends of the outbreak.