No Arabic abstract
Knowing COVID-19 epidemiological distributions, such as the time from patient admission to death, is directly relevant to effective primary and secondary care planning, and moreover, the mathematical modelling of the pandemic generally. We determine epidemiological distributions for patients hospitalised with COVID-19 using a large dataset ($N=21{,}000-157{,}000$) from the Brazilian Sistema de Informac{c}~ao de Vigil^ancia Epidemiologica da Gripe database. A joint Bayesian subnational model with partial pooling is used to simultaneously describe the 26 states and one federal district of Brazil, and shows significant variation in the mean of the symptom-onset-to-death time, with ranges between 11.2-17.8 days across the different states, and a mean of 15.2 days for Brazil. We find strong evidence in favour of specific probability density function choices: for example, the gamma distribution gives the best fit for onset-to-death and the generalised log-normal for onset-to-hospital-admission. Our results show that epidemiological distributions have considerable geographical variation, and provide the first estimates of these distributions in a low and middle-income setting. At the subnational level, variation in COVID-19 outcome timings are found to be correlated with poverty, deprivation and segregation levels, and weaker correlation is observed for mean age, wealth and urbanicity.
The transmission of COVID-19 is dependent on social contacts, the rate of which have varied during the pandemic due to mandated and voluntary social distancing. Changes in transmission dynamics eventually affect hospital admissions and we have used this connection in order to model and predict regional hospital admissions in Sweden during the COVID-19 pandemic. We use an SEIR-model for each region in Sweden in which the infectivity is assumed to depend on mobility data in terms of public transport utilisation and mobile phone usage. The results show that the model can capture the timing of the first and beginning of the second wave of the pandemic. Further, we show that for two major regions of Sweden models with public transport data outperform models using mobile phone usage. The model assumes a three week delay from disease transmission to hospitalisation which makes it possible to use current mobility data to predict future admissions.
We consider a continuous-time Markov chain model of SIR disease dynamics with two levels of mixing. For this so-called stochastic households model, we provide two methods for inferring the model parameters---governing within-household transmission, recovery, and between-household transmission---from data of the day upon which each individual became infectious and the household in which each infection occurred, as would be available from first few hundred studies. Each method is a form of Bayesian Markov Chain Monte Carlo that allows us to calculate a joint posterior distribution for all parameters and hence the household reproduction number and the early growth rate of the epidemic. The first method performs exact Bayesian inference using a standard data-augmentation approach; the second performs approximate Bayesian inference based on a likelihood approximation derived from branching processes. These methods are compared for computational efficiency and posteriors from each are compared. The branching process is shown to be an excellent approximation and remains computationally efficient as the amount of data is increased.
The SIR evolutionary model predicts too sharp a decrease of the fractions of people infected with COVID-19 in France after the start of the national lockdown, compared to what is observed. I fit the daily hospital data: arrivals in regular and critical care units, releases and deaths, using extended SEIR models. These involve ratios of evolutionary timescales to branching fractions, assumed uniform throughout a country, and the basic reproduction number, $R_0$, before and during the national lockdown, for each region of France. The joint-region Bayesian analysis allows precise evaluations of the time/fraction ratios and pre-hospitalized fractions. The hospital data are well fit by the models, except the arrivals in critical care, which decrease faster than predicted, indicating better treatment over time. Averaged over France, the analysis yields $R_0$= 3.4$pm$0.1 before the lockdown and 0.65$pm$0.04 (90% c.l.) during the lockdown, with small regional variations. On 11 May 2020, the Infection Fatality Rate in France was 4 $pm$1% (90% c.l.), while the Feverish vastly outnumber the Asymptomatic, contrary to the early phases. Without the lockdown nor social distancing, over 2 million deaths from COVID-19 would have occurred throughout France, while a lockdown that would have been enforced 10 days earlier would have led to less than 1000 deaths. The fraction of immunized people reached a plateau below 1% throughout France (3% in Paris) by late April 2020 (95% c.l.), suggesting a lack of herd immunity. The widespread availability of face masks on 11 May, when the lockdown was partially lifted, should keep $R_0$ below unity if at least 46% of the population wear them outside their home. Otherwise, without enhanced other social distancing, a second wave is inevitable and cause the number of deaths to triple between early May and October (if $R_0$=1.2) or even late June (if $R_0$=2).
Several analytical models have been used in this work to describe the evolution of death cases arising from coronavirus (COVID-19). The Death or `D model is a simplified version of the SIR (susceptible-infected-recovered) model, which assumes no recovery over time, and allows for the transmission-dynamics equations to be solved analytically. The D-model can be extended to describe various focuses of infection, which may account for the original pandemic (D1), the lockdown (D2) and other effects (Dn). The evolution of the COVID-19 pandemic in several countries (China, Spain, Italy, France, UK, Iran, USA and Germany) shows a similar behavior in concord with the D-model trend, characterized by a rapid increase of death cases followed by a slow decline, which are affected by the earliness and efficiency of the lockdown effect. These results are in agreement with more accurate calculations using the extended SIR model with a parametrized solution and more sophisticated Monte Carlo grid simulations, which predict similar trends and indicate a common evolution of the pandemic with universal parameters.
COVID-19 is a new pandemic disease that is affecting almost every country with a negative impact on social life and economic activities. The number of infected and deceased patients continues to increase globally. Mathematical models can help in developing better strategies to contain a pandemic. Considering multiple measures taken by African governments and challenging socio-economic factors, simple models cannot fit the data. We studied the dynamical evolution of COVID-19 in selected African countries. We derived a time-dependent reproduction number for each country studied to offer further insights into the spread of COVID-19 in Africa.