CoVID-19 in Singapore: Impact of Contact Tracing and Self-awareness on Healthcare Demand

AbstractBackgroundA great concern around the globe now is to mitigate the COVID-19 pandemic via contact tracing. Analyzing the control strategies during the first five months of 2020 in Singapore is important to estimate the effectiveness of contacting tracing measures.MethodsWe developed a mathematical model to simulate the COVID-19 epidemic in Singapore, with local cases stratified into 5 categories according to the conditions of contact tracing and self-awareness. Key parameters of each category were estimated from local surveillance data. We also simulated a set of possible scenarios to predict the effects of contact tracing and self-awareness for the following month.FindingsDuring January 23 - March 16, 2020, the success probabilities of contact tracing and self-awareness were estimated to be 31% (95% CI 28%-33%) and 54% (95% CI 51%-57%), respectively. During March 17 - April 7, 2020, several social distancing measures (e.g., limiting mass gathering) were introduced in Singapore, which, however, were estimated with minor contribution to reduce the non-tracing reproduction number per local case (Rι,2). If contact tracing and self-awareness cannot be further improved, we predict that the COVID-19 epidemic will continue to spread in Singapore if Rι,2 ≥ 1.5.ConclusionContact tracing and self-awareness can mitigate the COVID-19 transmission, and can be one of the key strategies to ensure a sustainable reopening after lifting the lockdown.SummaryWe evaluate the efficiency of contact tracing and self-awareness in Singapore’s early-stage control of COVID-19. Then use a branching model to simulate and evaluate the possible prospective outcomes of Singapore’s COVID-19 control in different scenarios.

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Mathematical modelling of COVID-19 transmission and control strategies in the population of Bauchi State, Nigeria

Annals of African Medical Research ◽

10.4081/aamr.2020.120 ◽

2020 ◽

Vol 3 (1) ◽

Author(s):

Yusuf Abdu Misau ◽

Nanshin Nansak ◽

Aliyu Maigoro ◽

Sani Malami ◽

Dominic Mogere ◽

...

Keyword(s):

Reproduction Number ◽

Control Strategies ◽

Research Work ◽

Control Measures ◽

High Rate ◽

World Health ◽

Contact Tracing ◽

Model Parameters ◽

Deterministic System ◽

The Novel

The novel SARS-COV-2 has since been declared a pandemic by the World Health Organization (WHO). The virus has spread from Wuhan city in China in December 2019 to no fewer than 200 countries as at June 2020 and still counting. Nigeria is currently experiencing a rapid spread of the virus amidst weak health system and more than 80% of population leaving on less than 1USD per day. To help understand the behavior of the virus in resource limited settings, we modelled the outbreak of COVID-19 and effects of control strategies in Bauchi state at north-eastern Nigeria. Using the real data of Bauchi state COVID-19 project, this research work extends the epidemic SEIR model by introducing new parameters based on the transmission dynamics of the novel COVID-19 pandemic and preventive measures. The total population of Bauchi State at the time of the study, given by is compartmentalized into five (5) different compartments as follows: Susceptible (S), Exposed (E), Infectious (I), Quarantined (Q) and Recovered (R). The new model is SEIQR. N = S → E → I → Q → R Data was collected by accessing Bauchi state electronic database of COVID-19 project to derive all the model parameters, while analysis and model building was done using Maple software. At the time of this study, it was found that the reproduction number R, for COVID-19 in Bauchi state, is 2.6 × 10-5. The reproduction number R decreased due to the application of control measures. The compartmental SEIRQ model in this study, which is a deterministic system of linear differential equations, has a continuum of disease-free equilibria, which is rigorously shown to be locallyasymptotically stable as the epidemiological threshold, known as the control reproduction number R= 0.0000026 is less than unity. The implication of this study is that the COVID-19 pandemic can be effectively controlled in Bauchi, since is R<1. Contact tracing and isolation must be increased as the models shows, the rise in infected class is a sign of high vulnerability of the population. Unless control measures are stepped up, despite high rate of recovery as shown by this study, infection rate will keep increasing as currently there is a no vaccine for COVID-19.

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Modeling the effects of contact tracing on COVID-19 transmission

Advances in Difference Equations ◽

10.1186/s13662-020-02972-8 ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Ali Traoré ◽

Fourtoua Victorien Konané

Keyword(s):

Mathematical Model ◽

Basic Reproduction Number ◽

Lyapunov Functions ◽

Reproduction Number ◽

Contact Tracing ◽

The Basic Reproduction Number

Abstract In this paper, a mathematical model for COVID-19 that involves contact tracing is studied. The contact tracing-induced reproduction number $\mathcal{R}_{q}$ R q and equilibrium for the model are determined and stabilities are examined. The global stabilities results are achieved by constructing Lyapunov functions. The contact tracing-induced reproduction number $\mathcal{R}_{q}$ R q is compared with the basic reproduction number $\mathcal{R}_{0}$ R 0 for the model in the absence of any intervention to assess the possible benefits of the contact tracing strategy.

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Analysis of a Model for Coronavirus Spread

Mathematics ◽

10.3390/math8050820 ◽

2020 ◽

Vol 8 (5) ◽

pp. 820 ◽

Cited By ~ 1

Author(s):

Youcef Belgaid ◽

Mohamed Helal ◽

Ezio Venturino

Keyword(s):

Dynamical System ◽

Mathematical Model ◽

Global Stability ◽

Basic Reproduction Number ◽

Local Stability ◽

Reproduction Number ◽

Early Stage ◽

Asymptomatic Individuals ◽

Restrictive Measures ◽

Disease Free

The spread of epidemics has always threatened humanity. In the present circumstance of the Coronavirus pandemic, a mathematical model is considered. It is formulated via a compartmental dynamical system. Its equilibria are investigated for local stability. Global stability is established for the disease-free point. The allowed steady states are an unlikely symptomatic-infected-free point, which must still be considered endemic due to the presence of asymptomatic individuals; and the disease-free and the full endemic equilibria. A transcritical bifurcation is shown to exist among them, preventing bistability. The disease basic reproduction number is calculated. Simulations show that contact restrictive measures are able to delay the epidemic’s outbreak, if taken at a very early stage. However, if lifted too early, they could become ineffective. In particular, an intermittent lock-down policy could be implemented, with the advantage of spreading the epidemics over a longer timespan, thereby reducing the sudden burden on hospitals.

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A hypothesis for the 2007 dengue outbreak in Singapore

Epidemiology and Infection ◽

10.1017/s0950268809990501 ◽

2009 ◽

Vol 138 (7) ◽

pp. 951-957 ◽

Cited By ~ 9

Author(s):

E. MASSAD ◽

F. A. B. COUTINHO ◽

S. MA ◽

M. N. BURATTINI

Keyword(s):

Mathematical Model ◽

Mortality Rate ◽

Carrying Capacity ◽

Reproduction Number ◽

Control Strategies ◽

Expected Number ◽

Alternative Control ◽

Dengue Outbreak ◽

Mosquito Mortality ◽

The Impact

SUMMARYA previous mathematical model explaining dengue in Singapore predicted a reasonable outbreak of about 6500 cases for 2006 and a very mild outbreak with about 2000 cases for 2007. However, only 3051 cases were reported in 2006 while more than 7800 were reported in the first 44 weeks of 2007. We hypothesized that the combination of haze with other local sources of particulate matter had a significant impact on mosquito life expectancy, significantly increasing their mortality rate. To test the hypothesis a mathematical model based on the reproduction number of dengue fever and aimed at comparing the impact of several possible alternative control strategies was proposed. This model also aimed at contributing to the understanding of the causes of dengue resurgence in Singapore in the last decade. The model's simulation demonstrated that an increase in mosquito mortality in 2006 and either a reduction in mortality or an increase in the carrying capacity of mosquitoes in 2007 explained the patterned observed in Singapore. Based on the model's simulation we concluded that the fewer than expected number of dengue cases in Singapore in 2006 was caused by an increase in mosquito mortality due to the disproportionate haze affecting the country that year and that particularly favourable environmental conditions in 2007 propitiated mosquitoes with a lower mortality rate, which explains the greater than expected number of dengue cases in 2007. Whether our hypothesis is plausible or not should be debated further.

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Stability Analysis and Optimal Control Strategy for Prevention of Pine Wilt Disease

Abstract and Applied Analysis ◽

10.1155/2014/182680 ◽

2014 ◽

Vol 2014 ◽

pp. 1-15 ◽

Cited By ~ 1

Author(s):

Kwang Sung Lee

Keyword(s):

Mathematical Model ◽

Optimal Control ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Control Strategies ◽

Pine Wilt Disease ◽

Wilt Disease ◽

Pine Wilt ◽

The Stability ◽

The Basic Reproduction Number

We propose a mathematical model of pine wilt disease (PWD) which is caused by pine sawyer beetles carrying the pinewood nematode (PWN). We calculate the basic reproduction numberR0and investigate the stability of a disease-free and endemic equilibrium in a given mathematical model. We show that the stability of the equilibrium in the proposed model can be controlled through the basic reproduction numberR0. We then discuss effective optimal control strategies for the proposed PWD mathematical model. We demonstrate the existence of a control problem, and then we apply both analytical and numerical techniques to demonstrate effective control methods to prevent the transmission of the PWD. In order to do this, we apply two control strategies: tree-injection of nematicide and the eradication of adult beetles through aerial pesticide spraying. Optimal prevention strategies can be determined by solving the corresponding optimality system. Numerical simulations of the optimal control problem using a set of reasonable parameter values suggest that reducing the number of pine sawyer beetles is more effective than the tree-injection strategy for controlling the spread of PWD.

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Stochastic discrete epidemic modeling of COVID-19 transmission in the Province of Shaanxi incorporating public health intervention and case importation

10.1101/2020.02.25.20027615 ◽

2020 ◽

Cited By ~ 7

Author(s):

Sanyi Tang ◽

Biao Tang ◽

Nicola Luigi Bragazzi ◽

Fan Xia ◽

Tangjuan Li ◽

...

Keyword(s):

Reproduction Number ◽

Public Health Intervention ◽

Shaanxi Province ◽

Contact Tracing ◽

Transmission Model ◽

Small Scale ◽

Cumulative Number ◽

Model Framework ◽

Local Case ◽

Discrete Epidemic Model

AbstractBefore the lock-down of Wuhan/Hubei/China, on January 23rd 2020, a large number of individuals infected by COVID-19 moved from the epicenter Wuhan and the Hubei province due to the Spring Festival, resulting in an epidemic in the other provinces including the Shaanxi province. The epidemic scale in Shaanxi was comparatively small and with half of cases being imported from the epicenter. Based on the complete epidemic data including the symptom onset time and transmission chains, we calculate the control reproduction number (1.48-1.69) in Xi’an. We could also compute the time transition, for each imported or local case, from the latent, to infected, to hospitalized compartment, as well as the effective reproduction number. This calculation enables us to revise our early deterministic transmission model to a stochastic discrete epidemic model with case importation and parameterize it. Our model-based analyses reveal that the newly generated infections decay to zero quickly; the cumulative number of case-driven quarantined individuals via contact tracing stabilize at a manageable level, indicating that the intervention strategies implemented in the Shaanxi province have been effective. Risk analyses, important for the consideration of “resumption of work”, show that a large second outbreak is expected if the level of case importation remains at the same level as between January 10th and February 4th 2020. However, if the case importation decreases by 30%, 60% and 90%, the second outbreak if happening will be of small-scale assuming contact tracing and quarantine/isolation remain as effective as before. Finally, we consider the effects of intermittent inflow with a Poisson distribution on the likelihood of multiple outbreaks. We believe the developed methodology and stochastic model provide an important model framework for the evaluation of revising travel restriction rules in the consideration of resuming social-economic activities while managing the disease control with potential case importation.

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A Mathematical Model Approach for Prevention and Intervention Measures of the COVID–19 Pandemic in Uganda

10.1101/2020.05.08.20095067 ◽

2020 ◽

Author(s):

Fulgensia Kamugisha Mbabazi ◽

Yahaya Gavamukulya ◽

Richard Awichi ◽

Peter Olupot–Olupot ◽

Samson Rwahwire ◽

...

Keyword(s):

Mathematical Model ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Virus Disease ◽

Transmission Rate ◽

Control Strategies ◽

Social Distancing ◽

Corona Virus ◽

The Impact ◽

The Basic Reproduction Number

AbstractThe human–infecting corona virus disease (COVID–19) caused by the novel severe acute respiratory syndrome corona virus 2 (SARS–CoV–2) was declared a global pandemic on March 11th, 2020. Current human deaths due to the infection have raised the threat globally with only 1 African country free of Virus (Lesotho) as of May 6th, 2020. Different countries have adopted different interventions at different stages of the outbreak, with social distancing being the first option while lock down the preferred option for flattening the curve at the peak of the pandemic. Lock down is aimed at adherence to social distancing, preserve the health system and improve survival. We propose a Susceptible–Exposed–Infected–Expected recoveries (SEIR) mathematical model to study the impact of a variety of prevention and control strategies Uganda has applied since the eruption of the pandemic in the country. We analyze the model using available data to find the infection–free, endemic/infection steady states and the basic reproduction number. In addition, a sensitivity analysis done shows that the transmission rate and the rate at which persons acquire the virus, have a positive influence on the basic reproduction number. On other hand the rate of evacuation by rescue ambulance greatly reduces the reproduction number. The results have potential to inform the impact and effect of early strict interventions including lock down in resource limited settings and social distancing.

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The importance of superspreaders on the spread of the global COVID-19 pandemic

10.21203/rs.3.rs-1167477/v1 ◽

2021 ◽

Author(s):

Jaan Kalda ◽

Mart Ratas ◽

Taavet Kalda ◽

Azer Ramazanli ◽

Heiko Herrmann ◽

...

Keyword(s):

Reproduction Number ◽

Early Stage ◽

Control Strategies ◽

Indirect Evidence ◽

Spreading Rate ◽

Rapid Decrease ◽

Scale Free ◽

The World ◽

Virus Spreading ◽

Key Parameter

Abstract The dynamics of pandemics is most often analyzed using a variation of the SIR (Susceptible-Infected-Recovered) model1, the key parameter of which is the basic reproduction number R0. Some evidences suggest that the contagion-spreading networks are scale-free, with the biggest nodes corresponding to superspreaders2,3. However, current understanding of the scale-free topology of these networks, and of the implications of such topology for the dynamics of pandemics is incomplete. Here we show that the world-wide spreading rate of COVID-19 gives an indirect evidence that the underlying virus-spreading network is scale-free, with the degree distribution exponent close to 2. Furthermore, our results show that the spreading rate of a virus is predominantly controlled by superspreaders who typically get infected and acquire immunity during the initial outbreak stage of the pandemic. Thereby the biggest nodes get immune and hence, removed from the network, resulting in a rapid decrease of the effective reproduction number. These findings are important for understanding the dynamics of pandemics, and for designing optimal virus control strategies. In particular, screening a population for the number of antibodies of a set of viruses can reveal potential superspreaders, the vaccination or isolation of whom can impede a pandemic at its early stage.

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On limits of contact tracing in epidemic control

PLoS ONE ◽

10.1371/journal.pone.0256180 ◽

2021 ◽

Vol 16 (8) ◽

pp. e0256180

Author(s):

Tomasz Piasecki ◽

Piotr B. Mucha ◽

Magdalena Rosińska

Keyword(s):

Deterministic Model ◽

Reproduction Number ◽

Early Stage ◽

Simple Rule ◽

Contact Tracing ◽

Epidemic Control ◽

Social Distancing ◽

Transmission Parameters ◽

Image Position ◽

The Impact

Contact tracing and quarantine are well established non-pharmaceutical epidemic control tools. The paper aims to clarify the impact of these measures in evolution of epidemic. The proposed deterministic model defines a simple rule on the reproduction number R in terms of ratio of diagnosed cases and, quarantine and transmission parameters. The model is applied to the early stage of Covid19 crisis in Poland. We investigate 3 scenarios corresponding to different ratios of diagnosed cases. Our results show that, depending on the scenario, contact tracing prevented from 50% to over 90% of cases. The effects of quarantine are limited by fraction of undiagnosed cases. The key conclusion is that under realistic assumptions the epidemic can not be controlled without any social distancing measures.

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Investigation of the Efficiency of Mask Wearing, Contact Tracing, and Case Isolation during the COVID-19 Outbreak

Journal of Clinical Medicine ◽

10.3390/jcm10132761 ◽

2021 ◽

Vol 10 (13) ◽

pp. 2761

Author(s):

Tatiana Filonets ◽

Maxim Solovchuk ◽

Wayne Gao ◽

Tony Wen-Hann Sheu

Keyword(s):

Mathematical Model ◽

Reproduction Number ◽

Control Measures ◽

Disease Spread ◽

Contact Tracing ◽

Imported Cases ◽

Quantitative Results ◽

High Level ◽

Pharmaceutical Interventions ◽

The Basic Reproduction Number

Case isolation and contact tracing are two essential parts of control measures to prevent the spread of COVID-19, however, additional interventions, such as mask wearing, are required. Taiwan successfully contained local COVID-19 transmission after the initial imported cases in the country in early 2020 after applying the above-mentioned interventions. In order to explain the containment of the disease spread in Taiwan and understand the efficiency of different non-pharmaceutical interventions, a mathematical model has been developed. A stochastic model was implemented in order to estimate the effectiveness of mask wearing together with case isolation and contact tracing. We investigated different approaches towards mask usage, estimated the effect of the interventions on the basic reproduction number (R0), and simulated the possibility of controlling the outbreak. With the assumption that non-medical and medical masks have 20% and 50% efficiency, respectively, case isolation works on 100%, 70% of all people wear medical masks, and R0 = 2.5, there is almost 80% probability of outbreak control with 60% contact tracing, whereas for non-medical masks the highest probability is only about 20%. With a large proportion of infectiousness before the onset of symptoms (40%) and the presence of asymptomatic cases, the investigated interventions (isolation of cases, contact tracing, and mask wearing by all people), implemented on a high level, can help to control the disease spread. Superspreading events have also been included in our model in order to estimate their impact on the outbreak and to understand how restrictions on gathering and social distancing can help to control the outbreak. The obtained quantitative results are in agreement with the empirical COVID-19 data in Taiwan.

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