Estimation of parameters for a humidity-dependent compartmental model of the COVID-19 outbreak

Abstract

Building an effective and highly usable epidemiology model presents two main challenges: finding the appropriate, realistic enough model that takes into account complex biological, social and environmental parameters and efficiently estimating the parameter values with which the model can accurately match the available outbreak data, provide useful projections. The reproduction number of the novel coronavirus (SARS-CoV-2) has been found to vary over time, potentially being influenced by a multitude of factors such as varying control strategies, changes in public awareness and reaction or, as a recent study suggests, sensitivity to temperature or humidity changes. To take into consideration these constantly evolving factors, the paper introduces a time dynamic, humidity-dependent SEIR-type extended epidemiological model with range-defined parameters. Using primarily the historical data of the outbreak from Northern and Southern Italy and with the help of stochastic global optimization algorithms, we are able to determine a model parameter estimation that provides a high-quality fit to the data. The time-dependent contact rate showed a quick drop to a value slightly below 2. Applying the model for the COVID-19 outbreak in the northern region of Italy, we obtained parameters that suggest a slower shrinkage of the contact rate to a value slightly above 4. These findings indicate that model fitting and validation, even on a limited amount of available data, can provide useful insights and projections, uncover aspects that upon improvement might help mitigate the disease spreading.

Keywords: COVID-19; Data fitting; Mathematical model; PSO algorithm; Parameter estimation SARS-nCoV-2.

Figure 1. Daily number of reported infectious cases in Northern (A) and Southern (B) Italy.

Figure 2. Model diagram for infection dynamics.

Figure 3. Input fields for the initial values of the differential equation system.

Figure 4. Interactive chart for temperature.

Figure 5. Data visualization based on the epidemiological model.

Figure 6. Infectious person count (blue & green bars) and the model’s data fitting (orange curves). (A) Northern Italy with 120 days training, 99 days validation. (B) Southern Italy with 120 days training and 99 days validation regions.

Figure 7. The Root Mean Square Error for the training (120 days) and validation (99 days) periods for for Northern Italy (A), and Southern Italy (B).

Figure 8. The graph of the function c(t), for Northern and Southern Italy.

Figure 9. Transmission probability, Northern Italy (A), South Italy (B).

Figure 10. The graph of the function R(t), Northern Italy (A), South Italy (B).

Figure 11. The graph of the function q(t), Northern (A) and Southern Italy (B).