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

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.

Identification of an Epidemiological Model to Simulate the COVID-19 Epidemic Using Robust Multiobjective Optimization and Stochastic Fractal Search.

Traditionally, the identification of parameters in the formulation and solution of inverse problems considers that models, variables, and mathematical parameters are free of uncertainties. This aspect simplifies the estimation process, but does not consider the influence of relatively small changes in the design variables in terms of the objective function. In this work, the SIDR (Susceptible, Infected, Dead, and Recovered) model is used to simulate the dynamic behavior of the novel coronavirus disease (COVID-19), and its parameters are estimated by formulating a robust inverse problem, that is, considering the sensitivity of design variables. For this purpose, a robust multiobjective optimization problem is formulated, considering the minimization of uncertainties associated with the estimation process and the maximization of the robustness parameter. To solve this problem, the Multiobjective Stochastic Fractal Search algorithm is associated with the Effective Mean concept for the evaluation of robustness. The results obtained considering real data of the epidemic in China demonstrate that the evaluation of the sensitivity of the design variables can provide more reliable results.

Determination of an optimal control strategy for vaccine administration in COVID-19 pandemic treatment.

BACKGROUND AND OBJECTIVE: For decades, mathematical models have been used to predict the behavior of physical and biological systems, as well as to define strategies aiming at the minimization of the effects regarding different types of diseases. In the present days, the development of mathematical models to simulate the dynamic behavior of the novel coronavirus disease (COVID-19) is considered an important theme due to the quantity of infected people worldwide. In this work, the objective is to determine an optimal control strategy for vaccine administration in COVID-19 pandemic treatment considering real data from China. Two optimal control problems (mono- and multi-objective) to determine a strategy for vaccine administration in COVID-19 pandemic treatment are proposed. The first consists of minimizing the quantity of infected individuals during the treatment. The second considers minimizing together the quantity of infected individuals and the prescribed vaccine concentration during the treatment. METHODS: An inverse problem is formulated and solved in order to determine the parameters of the compartmental Susceptible-Infectious-Removed model. The solutions for both optimal control problems proposed are obtained by using Differential Evolution and Multi-objective Optimization Differential Evolution algorithms. RESULTS: A comparative analysis on the influence related to the inclusion of a control strategy in the population subject to the epidemic is carried out, in terms of the compartmental model and its control parameters. The results regarding the proposed optimal control problems provide information from which an optimal strategy for vaccine administration can be defined. CONCLUSIONS: The solution of the optimal control problem can provide information about the effect of vaccination of a population in the face of an epidemic, as well as essential elements for decision making in the economic and governmental spheres.