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1.
Epidemiol Health ; 42: e2020047, 2020.
Article in English | MEDLINE | ID: covidwho-646722

ABSTRACT

OBJECTIVES: To estimate time-variant reproductive number (Rt) of coronavirus disease 19 based on either number of daily confirmed cases or their onset date to monitor effectiveness of quarantine policies. METHODS: Using number of daily confirmed cases from January 23, 2020 to March 22, 2020 and their symptom onset date from the official website of the Seoul Metropolitan Government and the district office, we calculated Rt using program R's package "EpiEstim". For asymptomatic cases, their symptom onset date was considered as -2, -1, 0, +1, and +2 days of confirmed date. RESULTS: Based on the information of 313 confirmed cases, the epidemic curve was shaped like 'propagated epidemic curve'. The daily Rt based on Rt_c peaked to 2.6 on February 20, 2020, then showed decreased trend and became <1.0 from March 3, 2020. Comparing both Rt from Rt_c and from the number of daily onset cases, we found that the pattern of changes was similar, although the variation of Rt was greater when using Rt_c. When we changed assumed onset date for asymptotic cases (-2 days to +2 days of the confirmed date), the results were comparable. CONCLUSIONS: Rt can be estimated based on Rt_c which is available from daily report of the Korea Centers for Disease Control and Prevention. Estimation of Rt would be useful to continuously monitor the effectiveness of the quarantine policy at the city and province levels.


Subject(s)
Basic Reproduction Number/statistics & numerical data , Coronavirus Infections/epidemiology , Epidemics , Pneumonia, Viral/epidemiology , Adolescent , Adult , Aged , Aged, 80 and over , Child , Coronavirus Infections/prevention & control , Female , Humans , Male , Middle Aged , Pandemics/prevention & control , Pneumonia, Viral/prevention & control , Public Policy , Quarantine , Seoul/epidemiology , Time Factors , Young Adult
2.
J Biol Dyn ; 14(1): 730-747, 2020 12.
Article in English | MEDLINE | ID: covidwho-740143

ABSTRACT

In this study, we estimate the severity of the COVID-19 outbreak in Pakistan prior to and after lockdown restrictions were eased. We also project the epidemic curve considering realistic quarantine, social distancing and possible medication scenarios. The pre-lock down value of R 0 is estimated to be 1.07 and the post lock down value is estimated to be 1.86. Using this analysis, we project the epidemic curve. We note that if no substantial efforts are made to contain the epidemic, it will peak in mid-September, 2020, with the maximum projected active cases being close to 700, 000. In a realistic, best case scenario, we project that the epidemic peaks in early to mid-July, 2020, with the maximum active cases being around 120, 000. We note that social distancing measures and medication will help flatten the curve; however, without the reintroduction of further lock down, it would be very difficult to make R 0 < 1 .


Subject(s)
Betacoronavirus , Coronavirus Infections/epidemiology , Disease Outbreaks , Pneumonia, Viral/epidemiology , Basic Reproduction Number/statistics & numerical data , Biostatistics , Coronavirus Infections/prevention & control , Coronavirus Infections/transmission , Disease Outbreaks/prevention & control , Disease Outbreaks/statistics & numerical data , Epidemics , Forecasting/methods , Humans , Mathematical Concepts , Models, Biological , Pakistan/epidemiology , Pandemics/prevention & control , Pneumonia, Viral/prevention & control , Pneumonia, Viral/transmission , Quarantine/statistics & numerical data
3.
Nat Commun ; 11(1): 4264, 2020 08 26.
Article in English | MEDLINE | ID: covidwho-733526

ABSTRACT

The pressing need to restart socioeconomic activities locked-down to control the spread of SARS-CoV-2 in Italy must be coupled with effective methodologies to selectively relax containment measures. Here we employ a spatially explicit model, properly attentive to the role of inapparent infections, capable of: estimating the expected unfolding of the outbreak under continuous lockdown (baseline trajectory); assessing deviations from the baseline, should lockdown relaxations result in increased disease transmission; calculating the isolation effort required to prevent a resurgence of the outbreak. A 40% increase in effective transmission would yield a rebound of infections. A control effort capable of isolating daily  ~5.5% of the exposed and highly infectious individuals proves necessary to maintain the epidemic curve onto the decreasing baseline trajectory. We finally provide an ex-post assessment based on the epidemiological data that became available after the initial analysis and estimate the actual disease transmission that occurred after weakening the lockdown.


Subject(s)
Communicable Disease Control/standards , Coronavirus Infections/epidemiology , Coronavirus Infections/prevention & control , Pandemics/prevention & control , Pneumonia, Viral/epidemiology , Pneumonia, Viral/prevention & control , Basic Reproduction Number , Betacoronavirus , Communicable Disease Control/trends , Coronavirus Infections/transmission , Forecasting , Geography , Hospitalization/statistics & numerical data , Hospitalization/trends , Humans , Italy/epidemiology , Models, Theoretical , Pneumonia, Viral/transmission , Social Isolation
4.
PLoS One ; 15(8): e0238090, 2020.
Article in English | MEDLINE | ID: covidwho-733001

ABSTRACT

In the article a virus transmission model is constructed on a simplified social network. The social network consists of more than 2 million nodes, each representing an inhabitant of Slovenia. The nodes are organised and interconnected according to the real household and elderly-care center distribution, while their connections outside these clusters are semi-randomly distributed and undirected. The virus spread model is coupled to the disease progression model. The ensemble approach with the perturbed transmission and disease parameters is used to quantify the ensemble spread, a proxy for the forecast uncertainty. The presented ongoing forecasts of COVID-19 epidemic in Slovenia are compared with the collected Slovenian data. Results show that at the end of the first epidemic wave, the infection was twice more likely to transmit within households/elderly care centers than outside them. We use an ensemble of simulations (N = 1000) and data assimilation approach to estimate the COVID-19 forecast uncertainty and to inversely obtain posterior distributions of model parameters. We found that in the uncontrolled epidemic, the intrinsic uncertainty mostly originates from the uncertainty of the virus biology, i.e. its reproduction number. In the controlled epidemic with low ratio of infected population, the randomness of the social network becomes the major source of forecast uncertainty, particularly for the short-range forecasts. Virus transmission models with accurate social network models are thus essential for improving epidemics forecasting.


Subject(s)
Computer Simulation , Coronavirus Infections/transmission , Pneumonia, Viral/transmission , Social Networking , Basic Reproduction Number , Betacoronavirus , Coronavirus Infections/epidemiology , Disease Progression , Family Characteristics , Forecasting , Humans , Models, Theoretical , Pandemics , Pneumonia, Viral/epidemiology , Slovenia/epidemiology , Uncertainty
5.
PLoS One ; 15(8): e0237832, 2020.
Article in English | MEDLINE | ID: covidwho-729563

ABSTRACT

This paper analyses the evolution of COVID-19 in Cameroon over the period March 6-April 2020 using SIR models. Specifically, we 1) evaluate the basic reproduction number of the virus, 2) determine the peak of the infection and the spread-out period of the disease, and 3) simulate the interventions of public health authorities. Data used in this study is obtained from the Cameroonian Public Health Ministry. The results suggest that over the identified period, the reproduction number of COVID-19 in Cameroon is about 1.5, and the peak of the infection should have occurred at the end of May 2020 with about 7.7% of the population infected. Furthermore, the implementation of efficient public health policies could help flatten the epidemic curve.


Subject(s)
Basic Reproduction Number , Coronavirus Infections/epidemiology , Disease Progression , Pneumonia, Viral/epidemiology , Algorithms , Betacoronavirus , Cameroon/epidemiology , Computer Simulation , Coronavirus Infections/prevention & control , Humans , Likelihood Functions , Models, Statistical , Pandemics/prevention & control , Pneumonia, Viral/prevention & control
6.
Bull Math Biol ; 82(9): 114, 2020 08 20.
Article in English | MEDLINE | ID: covidwho-725459

ABSTRACT

There is continued uncertainty in how long it takes a person infected by the COVID-19 virus to become infectious. In this paper, we quantify how this uncertainty affects estimates of the basic replication number [Formula: see text], and thus estimates of the fraction of the population that would become infected in the absence of effective interventions. The analysis is general, and applies to all SEIR-based models, not only those associated with COVID-19. We find that when modeling a rapidly spreading epidemic, seemingly minor differences in how latency is treated can lead to vastly different estimates of [Formula: see text]. We also derive a simple formula relating the replication number to the fraction of the population that is eventually infected. This formula is robust and applies to all compartmental models whose parameters do not depend on time.


Subject(s)
Basic Reproduction Number/statistics & numerical data , Betacoronavirus , Coronavirus Infections/transmission , Models, Biological , Pneumonia, Viral/transmission , Asymptomatic Infections/epidemiology , Coronavirus Infections/epidemiology , Coronavirus Infections/prevention & control , Humans , Immunity, Herd , Mathematical Concepts , Pandemics/prevention & control , Pandemics/statistics & numerical data , Pneumonia, Viral/epidemiology , Pneumonia, Viral/prevention & control , Time Factors , Uncertainty
7.
J Infect Dev Ctries ; 14(7): 713-720, 2020 Jul 31.
Article in English | MEDLINE | ID: covidwho-721539

ABSTRACT

INTRODUCTION: There are significant differences in the active cases and fatality rates of Covid-19 for different European countries. METHODOLOGY: The present study employs Monte Carlo based transmission growth simulations for Italy, Germany and Turkey. The probabilities of transmission at home, work and social networks and the number of initial cases have been calibrated to match the basic reproduction number and the reported fatality curves. Parametric studies were conducted to observe the effect of social distancing, work closure, testing and quarantine of the family and colleagues of positively tested individuals. RESULTS: It is observed that estimates of the number of initial cases in Italy compared to Turkey and Germany are higher. Turkey will probably experience about 30% less number of fatalities than Germany due its smaller elderly population. If social distancing and work contacts are limited to 25% of daily routines, Germany and Turkey may limit the number of fatalities to a few thousands as the reproduction number decreases to about 1.3 from 2.8. Random testing may reduce the number of fatalities by 10% upon testing least 5/1000 of the population. Quarantining of family and workmates of positively tested individuals may reduce the total number of fatalities by about 50%. CONCLUSIONS: The fatality rate of Covid-19 is estimated to be about 1.5% based on the simulation results. This may further be reduced by limiting the number of non-family contacts to two, conducting tests more than 0.5% of the population and immediate quarantine of the contacts for positively tested individuals.


Subject(s)
Coronavirus Infections/epidemiology , Coronavirus Infections/transmission , Pneumonia, Viral/epidemiology , Pneumonia, Viral/transmission , Quarantine , Adolescent , Adult , Age Distribution , Aged , Basic Reproduction Number , Child , Clinical Laboratory Techniques/statistics & numerical data , Coronavirus Infections/diagnosis , Coronavirus Infections/mortality , Family Characteristics , Germany/epidemiology , Humans , Italy/epidemiology , Middle Aged , Monte Carlo Method , Pandemics , Pneumonia, Viral/diagnosis , Pneumonia, Viral/mortality , Social Isolation , Social Networking , Turkey/epidemiology , Young Adult
8.
Epidemiol Infect ; 148: e166, 2020 08 05.
Article in English | MEDLINE | ID: covidwho-697050

ABSTRACT

Following the importation of coronavirus disease (COVID-19) into Nigeria on 27 February 2020 and then the outbreak, the question is: How do we anticipate the progression of the ongoing epidemic following all the intervention measures put in place? This kind of question is appropriate for public health responses and it will depend on the early estimates of the key epidemiological parameters of the virus in a defined population.In this study, we combined a likelihood-based method using a Bayesian framework and compartmental model of the epidemic of COVID-19 in Nigeria to estimate the effective reproduction number (R(t)) and basic reproduction number (R0) - this also enables us to estimate the initial daily transmission rate (ß0). We further estimate the reported fraction of symptomatic cases. The models are applied to the NCDC data on COVID-19 symptomatic and death cases from 27 February 2020 and 7 May 2020.In this period, the effective reproduction number is estimated with a minimum value of 0.18 and a maximum value of 2.29. Most importantly, the R(t) is strictly greater than one from 13 April till 7 May 2020. The R0 is estimated to be 2.42 with credible interval: (2.37-2.47). Comparing this with the R(t) shows that control measures are working but not effective enough to keep R(t) below 1. Also, the estimated fraction of reported symptomatic cases is between 10 and 50%.Our analysis has shown evidence that the existing control measures are not enough to end the epidemic and more stringent measures are needed.


Subject(s)
Basic Reproduction Number/statistics & numerical data , Coronavirus Infections/epidemiology , Coronavirus Infections/prevention & control , Epidemics/prevention & control , Pandemics/prevention & control , Pneumonia, Viral/epidemiology , Pneumonia, Viral/prevention & control , Public Health Practice , Bayes Theorem , Humans , Likelihood Functions , Nigeria/epidemiology
9.
Chaos ; 30(7): 071101, 2020 Jul.
Article in English | MEDLINE | ID: covidwho-695969

ABSTRACT

The ongoing novel coronavirus epidemic was announced a pandemic by the World Health Organization on March 11, 2020, and the Government of India declared a nationwide lockdown on March 25, 2020 to prevent community transmission of the coronavirus disease (COVID)-19. Due to the absence of specific antivirals or vaccine, mathematical modeling plays an important role in better understanding the disease dynamics and in designing strategies to control the rapidly spreading infectious disease. In our study, we developed a new compartmental model that explains the transmission dynamics of COVID-19. We calibrated our proposed model with daily COVID-19 data for four Indian states, namely, Jharkhand, Gujarat, Andhra Pradesh, and Chandigarh. We study the qualitative properties of the model, including feasible equilibria and their stability with respect to the basic reproduction number R0. The disease-free equilibrium becomes stable and the endemic equilibrium becomes unstable when the recovery rate of infected individuals increases, but if the disease transmission rate remains higher, then the endemic equilibrium always remains stable. For the estimated model parameters, R0>1 for all four states, which suggests the significant outbreak of COVID-19. Short-time prediction shows the increasing trend of daily and cumulative cases of COVID-19 for the four states of India.


Subject(s)
Coronavirus Infections/epidemiology , Coronavirus Infections/transmission , Pneumonia, Viral/epidemiology , Pneumonia, Viral/transmission , Algorithms , Basic Reproduction Number , Betacoronavirus , Calibration , Computer Simulation , Disease Outbreaks , Forecasting , Humans , India/epidemiology , Linear Models , Pandemics
10.
JAMA Netw Open ; 3(7): e2016818, 2020 07 01.
Article in English | MEDLINE | ID: covidwho-690937

ABSTRACT

Importance: The coronavirus disease 2019 (COVID-19) pandemic poses an existential threat to many US residential colleges; either they open their doors to students in September or they risk serious financial consequences. Objective: To define severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) screening performance standards that would permit the safe return of students to US residential college campuses for the fall 2020 semester. Design, Setting, and Participants: This analytic modeling study included a hypothetical cohort of 4990 students without SARS-CoV-2 infection and 10 with undetected, asymptomatic SARS-CoV-2 infection at the start of the semester. The decision and cost-effectiveness analyses were linked to a compartmental epidemic model to evaluate symptom-based screening and tests of varying frequency (ie, every 1, 2, 3, and 7 days), sensitivity (ie, 70%-99%), specificity (ie, 98%-99.7%), and cost (ie, $10/test-$50/test). Reproductive numbers (Rt) were 1.5, 2.5, and 3.5, defining 3 epidemic scenarios, with additional infections imported via exogenous shocks. The model assumed a symptomatic case fatality risk of 0.05% and a 30% probability that infection would eventually lead to observable COVID-19-defining symptoms in the cohort. Model projections were for an 80-day, abbreviated fall 2020 semester. This study adhered to US government guidance for parameterization data. Main Outcomes and Measures: Cumulative tests, infections, and costs; daily isolation dormitory census; incremental cost-effectiveness; and budget impact. Results: At the start of the semester, the hypothetical cohort of 5000 students included 4990 (99.8%) with no SARS-CoV-2 infection and 10 (0.2%) with SARS-CoV-2 infection. Assuming an Rt of 2.5 and daily screening with 70% sensitivity, a test with 98% specificity yielded 162 cumulative student infections and a mean isolation dormitory daily census of 116, with 21 students (18%) with true-positive results. Screening every 2 days resulted in 243 cumulative infections and a mean daily isolation census of 76, with 28 students (37%) with true-positive results. Screening every 7 days resulted in 1840 cumulative infections and a mean daily isolation census of 121 students, with 108 students (90%) with true-positive results. Across all scenarios, test frequency was more strongly associated with cumulative infection than test sensitivity. This model did not identify symptom-based screening alone as sufficient to contain an outbreak under any of the scenarios we considered. Cost-effectiveness analysis selected screening with a test with 70% sensitivity every 2, 1, or 7 days as the preferred strategy for an Rt of 2.5, 3.5, or 1.5, respectively, implying screening costs of $470, $910, or $120, respectively, per student per semester. Conclusions and Relevance: In this analytic modeling study, screening every 2 days using a rapid, inexpensive, and even poorly sensitive (>70%) test, coupled with strict behavioral interventions to keep Rt less than 2.5, is estimated to maintain a controllable number of COVID-19 infections and permit the safe return of students to campus.


Subject(s)
Coronavirus Infections/transmission , Disease Transmission, Infectious/prevention & control , Mass Screening , Pneumonia, Viral/transmission , Risk Assessment , Universities/organization & administration , Basic Reproduction Number , Betacoronavirus , Coronavirus Infections/epidemiology , Cost-Benefit Analysis , Humans , Mass Screening/economics , Pandemics , Patient Isolation , Pneumonia, Viral/epidemiology , Risk Assessment/economics , Sensitivity and Specificity , United States/epidemiology , Universities/economics
11.
PLoS One ; 15(7): e0236003, 2020.
Article in English | MEDLINE | ID: covidwho-689836

ABSTRACT

The emergence and fast global spread of COVID-19 has presented one of the greatest public health challenges in modern times with no proven cure or vaccine. Africa is still early in this epidemic, therefore the extent of disease severity is not yet clear. We used a mathematical model to fit to the observed cases of COVID-19 in South Africa to estimate the basic reproductive number and critical vaccination coverage to control the disease for different hypothetical vaccine efficacy scenarios. We also estimated the percentage reduction in effective contacts due to the social distancing measures implemented. Early model estimates show that COVID-19 outbreak in South Africa had a basic reproductive number of 2.95 (95% credible interval [CrI] 2.83-3.33). A vaccine with 70% efficacy had the capacity to contain COVID-19 outbreak but at very higher vaccination coverage 94.44% (95% Crl 92.44-99.92%) with a vaccine of 100% efficacy requiring 66.10% (95% Crl 64.72-69.95%) coverage. Social distancing measures put in place have so far reduced the number of social contacts by 80.31% (95% Crl 79.76-80.85%). These findings suggest that a highly efficacious vaccine would have been required to contain COVID-19 in South Africa. Therefore, the current social distancing measures to reduce contacts will remain key in controlling the infection in the absence of vaccines and other therapeutics.


Subject(s)
Coronavirus Infections/prevention & control , Coronavirus Infections/transmission , Models, Theoretical , Pandemics/prevention & control , Pneumonia, Viral/prevention & control , Pneumonia, Viral/transmission , Basic Reproduction Number , Betacoronavirus , Communicable Disease Control/methods , Humans , Social Isolation , South Africa/epidemiology , Vaccination Coverage , Viral Vaccines
13.
PLoS One ; 15(7): e0236620, 2020.
Article in English | MEDLINE | ID: covidwho-669612

ABSTRACT

The initial exponential growth rate of an epidemic is an important measure that follows directly from data at hand, commonly used to infer the basic reproduction number. As the growth rates λ(t) of tested positive COVID-19 cases have crossed the threshold in many countries, with negative numbers as surrogate for disease transmission deceleration, lockdowns lifting are linked to the behavior of the momentary reproduction numbers r(t), often called R0. Important to note that this concept alone can be easily misinterpreted as it is bound to many internal assumptions of the underlying model and significantly affected by the assumed recovery period. Here we present our experience, as part of the Basque Country Modeling Task Force (BMTF), in monitoring the development of the COVID-19 epidemic, by considering not only the behaviour of r(t) estimated for the new tested positive cases-significantly affected by the increased testing capacities, but also the momentary growth rates for hospitalizations, ICU admissions, deceased and recovered cases, in assisting the Basque Health Managers and the Basque Government during the lockdown lifting measures. Two different data sets, collected and then refined during the COVID-19 responses, are used as an exercise to estimate the momentary growth rates and reproduction numbers over time in the Basque Country, and the implications of using those concepts to make decisions about easing lockdown and relaxing social distancing measures are discussed. These results are potentially helpful for task forces around the globe which are now struggling to provide real scientific advice for health managers and governments while the lockdown measures are relaxed.


Subject(s)
Basic Reproduction Number , Coronavirus Infections/epidemiology , Pneumonia, Viral/epidemiology , Betacoronavirus , Coronavirus Infections/transmission , Hospitalization/statistics & numerical data , Humans , Intensive Care Units , Models, Theoretical , Pandemics , Pneumonia, Viral/transmission , Spain
14.
Emerg Infect Dis ; 26(7): 1470-1477, 2020 07.
Article in English | MEDLINE | ID: covidwho-668858

ABSTRACT

Severe acute respiratory syndrome coronavirus 2 is the causative agent of the ongoing coronavirus disease pandemic. Initial estimates of the early dynamics of the outbreak in Wuhan, China, suggested a doubling time of the number of infected persons of 6-7 days and a basic reproductive number (R0) of 2.2-2.7. We collected extensive individual case reports across China and estimated key epidemiologic parameters, including the incubation period (4.2 days). We then designed 2 mathematical modeling approaches to infer the outbreak dynamics in Wuhan by using high-resolution domestic travel and infection data. Results show that the doubling time early in the epidemic in Wuhan was 2.3-3.3 days. Assuming a serial interval of 6-9 days, we calculated a median R0 value of 5.7 (95% CI 3.8-8.9). We further show that active surveillance, contact tracing, quarantine, and early strong social distancing efforts are needed to stop transmission of the virus.


Subject(s)
Betacoronavirus , Coronavirus Infections/epidemiology , Pneumonia, Viral/epidemiology , Basic Reproduction Number , China/epidemiology , Coronavirus Infections/prevention & control , Coronavirus Infections/transmission , Disease Outbreaks , Humans , Models, Theoretical , Pandemics/prevention & control , Pneumonia, Viral/prevention & control , Pneumonia, Viral/transmission , Travel
15.
JAMA Netw Open ; 3(7): e2016099, 2020 07 01.
Article in English | MEDLINE | ID: covidwho-665306

ABSTRACT

Importance: Local variation in the transmission of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) across the United States has not been well studied. Objective: To examine the association of county-level factors with variation in the SARS-CoV-2 reproduction number over time. Design, Setting, and Participants: This cohort study included 211 counties, representing state capitals and cities with at least 100 000 residents and including 178 892 208 US residents, in 46 states and the District of Columbia between February 25, 2020, and April 23, 2020. Exposures: Social distancing, measured by percentage change in visits to nonessential businesses; population density; and daily wet-bulb temperatures. Main Outcomes and Measures: Instantaneous reproduction number (Rt), or cases generated by each incident case at a given time, estimated from daily case incidence data. Results: The 211 counties contained 178 892 208 of 326 289 971 US residents (54.8%). Median (interquartile range) population density was 1022.7 (471.2-1846.0) people per square mile. The mean (SD) peak reduction in visits to nonessential business between April 6 and April 19, as the country was sheltering in place, was 68.7% (7.9%). Median (interquartile range) daily wet-bulb temperatures were 7.5 (3.8-12.8) °C. Median (interquartile range) case incidence and fatality rates per 100 000 people were approximately 10 times higher for the top decile of densely populated counties (1185.2 [313.2-1891.2] cases; 43.7 [10.4-106.7] deaths) than for counties in the lowest density quartile (121.4 [87.8-175.4] cases; 4.2 [1.9-8.0] deaths). Mean (SD) Rt in the first 2 weeks was 5.7 (2.5) in the top decile compared with 3.1 (1.2) in the lowest quartile. In multivariable analysis, a 50% decrease in visits to nonessential businesses was associated with a 45% decrease in Rt (95% CI, 43%-49%). From a relative Rt at 0 °C of 2.13 (95% CI, 1.89-2.40), relative Rt decreased to a minimum as temperatures warmed to 11 °C, increased between 11 and 20 °C (1.61; 95% CI, 1.42-1.84) and then declined again at temperatures greater than 20 °C. With a 70% reduction in visits to nonessential business, 202 counties (95.7%) were estimated to fall below a threshold Rt of 1.0, including 17 of 21 counties (81.0%) in the top density decile and 52 of 53 counties (98.1%) in the lowest density quartile.2. Conclusions and Relevance: In this cohort study, social distancing, lower population density, and temperate weather were associated with a decreased Rt for SARS-CoV-2 in counties across the United States. These associations could inform selective public policy planning in communities during the coronavirus disease 2019 pandemic.


Subject(s)
Basic Reproduction Number , Coronavirus Infections/epidemiology , Pandemics , Pneumonia, Viral/epidemiology , Population Density , Social Distance , Temperature , Betacoronavirus , Coronavirus Infections/transmission , Disease Transmission, Infectious/prevention & control , Epidemiological Monitoring , Humans , Incidence , Pneumonia, Viral/transmission , United States/epidemiology
16.
J R Soc Interface ; 17(168): 20200144, 2020 07.
Article in English | MEDLINE | ID: covidwho-665024

ABSTRACT

A novel coronavirus (SARS-CoV-2) emerged as a global threat in December 2019. As the epidemic progresses, disease modellers continue to focus on estimating the basic reproductive number [Formula: see text]-the average number of secondary cases caused by a primary case in an otherwise susceptible population. The modelling approaches and resulting estimates of [Formula: see text] during the beginning of the outbreak vary widely, despite relying on similar data sources. Here, we present a statistical framework for comparing and combining different estimates of [Formula: see text] across a wide range of models by decomposing the basic reproductive number into three key quantities: the exponential growth rate, the mean generation interval and the generation-interval dispersion. We apply our framework to early estimates of [Formula: see text] for the SARS-CoV-2 outbreak, showing that many [Formula: see text] estimates are overly confident. Our results emphasize the importance of propagating uncertainties in all components of [Formula: see text], including the shape of the generation-interval distribution, in efforts to estimate [Formula: see text] at the outset of an epidemic.


Subject(s)
Basic Reproduction Number , Betacoronavirus , Coronavirus Infections/epidemiology , Coronavirus Infections/transmission , Disease Outbreaks , Models, Biological , Pneumonia, Viral/epidemiology , Pneumonia, Viral/transmission , Basic Reproduction Number/statistics & numerical data , Bayes Theorem , China/epidemiology , Disease Outbreaks/statistics & numerical data , Epidemics/statistics & numerical data , Humans , Markov Chains , Monte Carlo Method , Pandemics , Probability , Uncertainty
17.
J Biol Dyn ; 14(1): 590-607, 2020 12.
Article in English | MEDLINE | ID: covidwho-664401

ABSTRACT

In this paper, we apply optimal control theory to a novel coronavirus (COVID-19) transmission model given by a system of non-linear ordinary differential equations. Optimal control strategies are obtained by minimizing the number of exposed and infected population considering the cost of implementation. The existence of optimal controls and characterization is established using Pontryagin's Maximum Principle. An expression for the basic reproduction number is derived in terms of control variables. Then the sensitivity of basic reproduction number with respect to model parameters is also analysed. Numerical simulation results demonstrated good agreement with our analytical results. Finally, the findings of this study shows that comprehensive impacts of prevention, intensive medical care and surface disinfection strategies outperform in reducing the disease epidemic with optimum implementation cost.


Subject(s)
Betacoronavirus , Coronavirus Infections/prevention & control , Coronavirus Infections/transmission , Models, Biological , Pandemics/prevention & control , Pneumonia, Viral/prevention & control , Pneumonia, Viral/transmission , Basic Reproduction Number/statistics & numerical data , Computer Simulation , Coronavirus Infections/epidemiology , Epidemics/prevention & control , Epidemics/statistics & numerical data , Humans , Infection Control , Mathematical Concepts , Nonlinear Dynamics , Pneumonia, Viral/epidemiology , Risk Factors , Systems Biology
18.
Rev. salud pública ; 22(2): e286432, mar.-abr. 2020. tab, graf
Article in Spanish | LILACS (Americas) | ID: covidwho-664970

ABSTRACT

RESUMEN Objetivo Predecir el número de casos de COVID-19 en la ciudad de Cali-Colombia mediante el desarrollo de un modelo SEIR. Métodos Se utilizó un modelo determinista compartimental SEIR considerando los estados: susceptibles (S), expuestos (E), infectados (I) y recuperados (R). Los parámetros del modelo fueron seleccionados de acuerdo a la revisión de literatura. En el caso de la tasa de letalidad, se usaron los datos de la Secretaría de Salud Municipal de Cali. Se plantearon varios escenarios teniendo en cuenta variaciones en el número básico de reproducción (R0) y en la tasa de letalidad; además, se comparó la predicción hasta el 9 de abril con los datos observados. Resultados A través del modelo SEIR se encontró que, con el número básico de reproducción más alto (2,6) y utilizando la letalidad calculada para la ciudad de 2,0%, el número máximo de casos se alcanzaría el primero de junio con 195 666 (prevalencia); sin embargo, al comparar los casos observados con los esperados, al inicio la ocurrencia observada estaba por encima de la proyectada; pero luego cambia la tendencia con una disminución marcada de la pendiente. Conclusiones Los modelos epidemiológicos SEIR son métodos muy utilizados para la proyección de casos en enfermedades infecciosas; sin embargo, se debe tener en cuenta que son modelos deterministas que pueden utilizar parámetros supuestos y podrían generar resultados imprecisos.(AU)


ABSTRACT Objective To predict the number of cases of COVID-19 in the city of Cali-Colombia through the development of a SEIR model. Methods A SEIR compartmental deterministic model was used considering the states: susceptible (S), exposed (E), infected (I) and recovered (R). The model parameters were selected according to the literature review, in the case of the case fatality rate data from the Municipal Secretary of Health were used. Several scenarios were considered taking into account variations in the basic number of reproduction (R0), and the prediction until april 9 was compared with the observed data. Results Through the SEIR model it was found that with the highest basic number of reproduction [2,6] and using the case fatality rate for the city of 2,0%, the maximum number of cases would be reached on June 1 with 195 666 (prevalence). However, when comparing the observed with the expected cases, at the beginning the observed occurrence was above the projected, but then the trend changes decreasing the slope. Conclusions SEIR epidemiological models are widely used methods for projecting cases in infectious diseases, however it must be taken into account that they are deterministic models that can use assumed parameters and could generate imprecise results.(AU)


Subject(s)
Humans , Coronavirus Infections/epidemiology , Basic Reproduction Number/statistics & numerical data , Pandemics/statistics & numerical data , Colombia/epidemiology , Forecasting
19.
Rev. salud pública ; 22(1): e185977, ene.-feb. 2020. tab, graf
Article in Spanish, Portuguese | LILACS (Americas) | ID: covidwho-664613

ABSTRACT

RESUMEN Objetivo Desarrollar un modelo SIR pronóstico de la pandemia de COVID-19 en el territorio colombiano. Métodos Se utilizó un modelo SIR con enfoque determinístico para pronosticar el desarrollo de la pandemia de COVID-19 en Colombia. Los estados considerados fueron susceptibles (S), infecciosos (i) y recuperados o fallecidos (R). Los datos poblacionales se obtuvieron del Departamento Administrativo Nacional de estadística (Proyecciones de Población 2018-2020, difundida en enero de 2020) y los datos sobre casos diarios confirmados de COVID-19 del Instituto Nacional de Salud. Se plantearon diferentes modelos variando el número básico de reproducción (R0). Resultados A partir de los casos reportados por el Ministerio de Salud se crearon cuatro ambientes o escenarios simulados en un modelo SIR epidemiológico, se extendieron las series de tiempo hasta el 30 de mayo, fecha probable del 99% de infección poblacional. Un R0 de 2 es la aproximación más cercana al comportamiento de la pandemia durante los primeros 15 días desde el reporte del caso 0, el peor escenario se daría en la primera semana de abril con un R0 igual a 3. Conclusiones Se hacen necesarias nuevas medidas de mitigación y supresión en las fases de contención y transmisión sostenida, como aumento de la capacidad diagnostica por pruebas y desinfección de zonas pobladas y hogares de aislamiento.


ABSTRACT Objective To develop a prognostic SIR model of the COVID-19 pandemic in Colombia. Materials and Methods A SIR model with a deterministic approach was used to forecast the development of the COVID-19 pandemic in Colombia. The states considered were susceptible (S), infectious (i) and recovered or deceased (R). Population data were obtained from the National Administrative Department of Statistics (DANE) - Population Projections 2018-2020, released in January 2020-, and data on daily confirmed cases of COVID-19 from the National Institute of Health. Different models were proposed varying the basic reproduction number (R0). Results Based on the cases reported by the Ministry of Health, 4 simulated environments were created in an epidemiological SIR model. The time series was extended until May 30, the probable date when 99% of the population will be infected. R0=2 is the basic reproduction number and the closest approximation to the behavior of the pandemic during the first 15 days since the first case report; the worst scenario would occur in the first week of April with R0=3. Conclusions Further mitigation and suppression measures are necessary in the containment and sustained transmission phases, such as increased diagnostic capacity through testing and disinfection of populated areas and homes in isolation.


RESUMO OBJETIVO Desenvolver um modelo SIR prognóstico da pandemia de COVID-19 no território colombiano. MÉTODOS Um modelo SIR com abordagem determinística foi usado para prever o desenvolvimento da pandemia de COVID-19 na Colômbia. Os estados considerados foram suscetíveis (S), infecciosos (i) e recuperados ou falecidos (R). Os dados populacionais foram obtidos do Departamento Administrativo Nacional de Estatística (Projeções de População 2018-2020, divulgado em janeiro de 2020) e dados sobre casos confirmados diariamente de COVID-19 do Instituto Nacional de Saúde. Diferentes modelos foram propostos variando o número básico de reprodução (R 0 ). RESULTADOS Dos casos relatados pelo Ministério da Saúde, quatro ambientes ou cenários simulados foram criados em um modelo epidemiológico de RIS, as séries temporais foram estendidas até 30 de maio, data provável de 99% de infecção populacional. Um R 0 de 2 é a aproximação mais próxima do comportamento da pandemia durante os primeiros 15 dias a partir do relato do caso 0, o pior cenário ocorreria na primeira semana de abril com um R 0 igual a 3. CONCLUSÕES Novas medidas de mitigação e supressão são necessárias nas fases de contenção e transmissão sustentada, como aumento da capacidade de diagnóstico por testes e desinfecção de áreas povoadas e residências isoladas.


Subject(s)
Humans , Coronavirus Infections/transmission , Coronavirus Infections/epidemiology , Prevention and Mitigation/methods , Basic Reproduction Number , Pandemics , Colombia/epidemiology
20.
PLoS One ; 15(7): e0236464, 2020.
Article in English | MEDLINE | ID: covidwho-659386

ABSTRACT

The coronavirus pandemic has rapidly evolved into an unprecedented crisis. The susceptible-infectious-removed (SIR) model and its variants have been used for modeling the pandemic. However, time-independent parameters in the classical models may not capture the dynamic transmission and removal processes, governed by virus containment strategies taken at various phases of the epidemic. Moreover, few models account for possible inaccuracies of the reported cases. We propose a Poisson model with time-dependent transmission and removal rates to account for possible random errors in reporting and estimate a time-dependent disease reproduction number, which may reflect the effectiveness of virus control strategies. We apply our method to study the pandemic in several severely impacted countries, and analyze and forecast the evolving spread of the coronavirus. We have developed an interactive web application to facilitate readers' use of our method.


Subject(s)
Basic Reproduction Number , Coronavirus Infections/epidemiology , Forecasting , Models, Statistical , Pneumonia, Viral/epidemiology , Betacoronavirus , Coronavirus Infections/transmission , Humans , Pandemics , Pneumonia, Viral/transmission , Time Factors
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