COVID-19: Estimation of the transmission dynamics in Spain using a stochastic simulator and black-box optimization techniques

Abstract

Background and objectives: Epidemiological models of epidemic spread are an essential tool for optimizing decision-making. The current literature is very extensive and covers a wide variety of deterministic and stochastic models. However, with the increase in computing resources, new, more general, and flexible procedures based on simulation models can assess the effectiveness of measures and quantify the current state of the epidemic. This paper illustrates the potential of this approach to build a new dynamic probabilistic model to estimate the prevalence of SARS-CoV-2 infections in different compartments.

Methods: We propose a new probabilistic model in which, for the first time in the epidemic literature, parameter learning is carried out using gradient-free stochastic black-box optimization techniques simulating multiple trajectories of the infection dynamics in a general way, solving an inverse problem that is defined employing the daily information from mortality records.

Results: After the application of the new proposal in Spain in the first and successive waves, the result of the model confirms the accuracy to estimate the seroprevalence and allows us to know the real dynamics of the pandemic a posteriori to assess the impact of epidemiological measures by the Spanish government and to plan more efficiently the subsequent decisions with the prior knowledge obtained.

Conclusions: The model results allow us to estimate the daily patterns of COVID-19 infections in Spain retrospectively and examine the population's exposure to the virus dynamically in contrast to seroprevalence surveys. Furthermore, given the flexibility of our simulation framework, we can model situations -even using non-parametric distributions between the different compartments in the model- that other models in the existing literature cannot. Our general optimization strategy remains valid in these cases, and we can easily create other non-standard simulation epidemic models that incorporate more complex and dynamic structures.

Keywords: COVID-19; Computing science; Epidemic models; Evolutionary computations; Stochastic processes.

Fig. 1

Diagram of state changes in our model.

Fig. 2

Spread and number of deaths of Coronavirus in Spain, Italy, China, and the United States. Number of accumulated infected patients (left) and the number of accumulated deaths (right) .

Fig. 3

Evolution of accumulated infected (left) and death patients (right) in Galicia, País Vasco, Castilla y León, Madrid, Cataluña.

Fig. 4

Results in Madrid.

Fig. 5

Results in Galicia.

Fig. 6

Results in Spain.

Fig. 7

Dynamic evolution of the number of active infections in the Spanish population (top Figure). Daily cases reported by the Spanish government (middle Figure). The day-to-day percentage of active infections in the Spanish population by health agencies (bottom Figure).