Mathematical modelling of the second wave of COVID-19 infections using deterministic and stochastic SIDR models

Abstract

Recently, various countries from across the globe have been facing the second wave of COVID-19 infections. In order to understand the dynamics of the spread of the disease, much effort has been made in terms of mathematical modeling. In this scenario, compartmental models are widely used to simulate epidemics under various conditions. In general, there are uncertainties associated with the reported data, which must be considered when estimating the parameters of the model. In this work, we propose an effective methodology for estimating parameters of compartmental models in multiple wave scenarios by means of a dynamic data segmentation approach. This robust technique allows the description of the dynamics of the disease without arbitrary choices for the end of the first wave and the start of the second. Furthermore, we adopt a time-dependent function to describe the probability of transmission by contact for each wave. We also assess the uncertainties of the parameters and their influence on the simulations using a stochastic strategy. In order to obtain realistic results in terms of the basic reproduction number, a constraint is incorporated into the problem. We adopt data from Germany and Italy, two of the first countries to experience the second wave of infections. Using the proposed methodology, the end of the first wave (and also the start of the second wave) occurred on 166 and 187 days from the beginning of the epidemic, for Germany and Italy, respectively. The estimated effective reproduction number for the first wave is close to that obtained by other approaches, for both countries. The results demonstrate that the proposed methodology is able to find good estimates for all parameters. In relation to uncertainties, we show that slight variations in the design variables can give rise to significant changes in the value of the effective reproduction number. The results provide information on the characteristics of the epidemic for each country, as well as elements for decision-making in the economic and governmental spheres.

The starting dates of COVID-19 multiple waves

“…Several mathematical approaches can be used to access the dynamics of an epidemic wave, including the estimation of their initial date. Compartmental models [18][19][20] based on differential equations are very natural for this purpose, with the underling parametrization obtained with aid of dataassimilation techniques, such as Kalman filter 21 , nonlinear regression [22][23][24][25] , Bayesian statistics 26,27 , neural networks and other machine learning tools [28][29][30][31] , etc. 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] .…”

Regional opening strategies with commuter testing and containment of new SARS-CoV-2 variants in Germany

“…Some obvious limitations of simple ODE-SIR-type models are the homogeneous mixing assumption, the lack of stochastic effects and the implicit use of exponentially distributed compartment stays. The authors of [ 26 ] considered stochastic and deterministic ODE-SIR-type models and [ 27 ] provides an overview over 13, either stochastic or deterministic, models from 33 papers. The authors of [ 28 ] used stochastic compartment models to consider the effect of NPIs and [ 29 ] used a stochastic branching process which may be advantageous over compartment models in the beginning phase of pandemic.…”

Data analysis and prediction of the COVID-19 outbreak in the first and second waves for top 5 affected countries in the world

“…Very recently, Kuddus and Rahman [ 2 ] have used the improved SLIR model with nonlinear incidence, and they have observed that the transmission rate of each parameter had a significant impact on COVID-19. Lobato et al [ 3 ] proposed a dynamic data segmentation approach to provide reasonable estimates for all parameters. A three-party differential game model including epidemic prevention and risk coefficient was proposed by [ 14 ], and results were presented based on theoretical and numerical analysis.…”

“…Recently, many researchers have studied mathematical modeling of COVID-19 for second waves (Iftimie et al, [ 31 ]; Vasconcelos et al, [ 32 ]; Salyer et al, [ 33 ]; Lobato et al, [ 3 ]). The so-called second wave of COVID-19 is characterized by an expressive increase in the number of confirm cases after a significant drop in the number of new infections during the first wave.…”