No Arabic abstract
In times of outbreaks, an essential requirement for better monitoring is the evaluation of the number of undiagnosed infected individuals. An accurate estimate of this fraction is crucial for the assessment of the situation and the establishment of protective measures. In most current studies using epidemics models, the total number of infected is either approximated by the number of diagnosed individuals or is dependent on the model parameters and assumptions, which are often debated. We here study the relationship between the fraction of diagnosed infected out of all infected, and the fraction of infected with known contaminator out of all diagnosed infected. We show that those two are approximately the same in exponential models and across most models currently used in the study of epidemics, independently of the model parameters. As an application, we compute an estimate of the effective number of infected by the SARS-CoV-2 virus in various countries.
Some ideas are presented about the physical motivation of the apparent capacity of generalized logistic equations to describe the outbreak of the COVID-19 infection, and in general of quite many other epidemics. The main focuses here are: the complex, possibly fractal, structure of the locus describing the contagion event set; what can be learnt from the models of trophic webs with herd behaviour.
This article contains a series of analyses done for the SARS-CoV-2 outbreak in Rio Grande do Sul (RS) in the south of Brazil. These analyses are focused on the high-incidence cities such as the state capital Porto Alegre and at the state level. We provide methodological details and estimates for the effective reproduction number $R_t$, a joint analysis of the mobility data together with the estimated $R_t$ as well as ICU simulations and ICU LoS (length of stay) estimation for hospitalizations in Porto Alegre/RS.
The COVID-19 pandemic has demonstrated how disruptive emergent disease outbreaks can be and how useful epidemic models are for quantifying risks of local outbreaks. Here we develop an analytical approach to calculate the dynamics and likelihood of outbreaks within the canonical Susceptible-Exposed-Infected-Recovered and more general models, including COVID-19 models, with fixed population sizes. We compute the distribution of outbreak sizes including extreme events, and show that each outbreak entails a unique, depletion or boost in the pool of susceptibles and an increase or decrease in the effective recovery rate compared to the mean-field dynamics -- due to finite-size noise. Unlike extreme events occurring in long-lived metastable stochastic systems, the underlying outbreak distribution depends on a full continuum of optimal paths, each connecting two unique non-trivial fixed-points, and thus represents a novel class of extreme dynamics.
We propose a novel testing and containment strategy in order to contain the spread of SARS-CoV2 while permitting large parts of the population to resume social and economic activity. Our approach recognises the fact that testing capacities are severely constrained in many countries. In this setting, we show that finding the best way to utilise this limited number of tests during a pandemic can be formulated concisely as an allocation problem. Our problem formulation takes into account the heterogeneity of the population and uses pooled testing to identify and isolate individuals while prioritising key workers and individuals with a higher risk of spreading the disease. In order to demonstrate the efficacy of our testing and containment mechanism, we perform simulations using a network-based SIR model. Our simulations indicate that applying our mechanism on a population of $100,000$ individuals with only $16$ tests per day reduces the peak number of infected individuals by approximately $20%$, when compared to the scenario where no intervention is implemented.
We consider a single outbreak susceptible-infected-recovered (SIR) model and corresponding estimation procedures for the effective reproductive number $mathcal{R}(t)$. We discuss the estimation of the underlying SIR parameters with a generalized least squares (GLS) estimation technique. We do this in the context of appropriate statistical models for the measurement process. We use asymptotic statistical theories to derive the mean and variance of the limiting (Gaussian) sampling distribution and to perform post statistical analysis of the inverse problems. We illustrate the ideas and pitfalls (e.g., large condition numbers on the corresponding Fisher information matrix) with both synthetic and influenza incidence data sets.