A stochastic Bayesian bootstrapping model for COVID-19 data

Abstract

We provide a stochastic modeling framework for the incidence of COVID-19 in Castilla-Leon (Spain) for the period March 1, 2020 to February 12, 2021, which encompasses four waves. Each wave is appropriately described by a generalized logistic growth curve. Accordingly, the four waves are modeled through a sum of four generalized logistic growth curves. Pointwise values of the twenty input parameters are fitted by a least-squares optimization procedure. Taking into account the significant variability in the daily reported cases, the input parameters and the errors are regarded as random variables on an abstract probability space. Their probability distributions are inferred from a Bayesian bootstrap procedure. This framework is shown to offer a more accurate estimation of the COVID-19 reported cases than the deterministic formulation.

The starting dates of COVID-19 multiple waves

“…Such compartmental models are also fundamental in approaches that employ the concept of complex networks to describe the epidemic dynamics in a large population with heterogeneous spatial distribution [32][33][34][35][36] . It is also quite common to describe the evolution of epidemic waves with aid of purely phenomenological models, supported by frequentist [37][38][39][40][41][42][43][44][45] or Bayesian 46,47 statistical approaches.…”

Spatio-temporal stochastic differential equations for crime incidence modeling

“…These types of models have certainly been considered in environmental sciences (Calatayud et al. 2022 , 2023b ; Chowell et al. 2016 ; Nafidi et al.…”

“…Further, it includes spatial correlations in the formulation, in contrast to similar stochastic models (Calatayud et to assess the evolution of social behaviors. These types of models have certainly been considered in environmental sciences (Calatayud et al 2022(Calatayud et al , 2023bChowell et al 2016;Nafidi et al 2022;Pell et al 2018) (Zika, Ebola, COVID-19 and CO 2 emissions, with certain exponential growths) and turn out to be successful in our context of offenses. Nevertheless, phenomenological forecasting models are limited by the assumption that future incidence will follow the patterns of incidence observed in the past.…”

“…However, the solution stochastic process x t ¼ x 0 e lt would not be irregular in such a formulation, but smooth (Neckel and Rupp 2013). This issue could be fixed by incorporating a certain random model error E t , with resulting response process x t ¼ x 0 e lt þ E t , and then applying Bayesian or maximum-likelihood inference for parameter estimation (Calatayud and Jornet 2020;Calatayud et al 2022Calatayud et al , 2023bSmith 2013;Xiu 2010). Nonetheless, a certain structure of the residuals of the deterministic exponential model would then be required, for example, symmetry around zero, homoscedasticity, etc.…”

Modeling noisy time-series data of crime with stochastic differential equations

“…( 2018 ) employ logistic differential equations to forecast the burden of Zika and Ebola epidemics, respectively; Calatayud et al. ( 2022 ) proposes multiple stochastic logistic functions to fit several COVID-19 waves and forecast; and Nafidi et al. ( 2022 ) studies the applicability of a stochastic modified Lundqvist–Korf diffusion process to model emissions.…”