A Modeling Study on the Effect of Interstate Mobility Restrictions on the SARS-CoV-2 Pandemic.

Mobility is a crucial element in comprehending the possible expansion of the transmission chain in an epidemic. In the initial phases, strategies for containing cases can be directly linked to population mobility restrictions, especially when only non-pharmaceutical measures are available. During the pandemic of COVID-19 in Brazil, mobility limitation measures were strongly opposed by a large portion of the population. Hypothetically, if the population had supported such measures, the sharp rise in the number of cases could have been suppressed. In this context, computational modeling offers systematic methods for analyzing scenarios about the development of the epidemiological situation taking into account specific conditions. In this study, we examine the impacts of interstate mobility in Brazil. To do so, we develop a metapopulational model that considers both intra and intercompartmental dynamics, utilizing graph theory. We use a parameter estimation technique that allows us to infer the effective reproduction number in each state and estimate the time-varying transmission rate. This makes it possible to investigate scenarios related to mobility and quantify the effect of people moving between states and how certain measures to limit movement might reduce the impact of the pandemic. Our results demonstrate a clear association between the number of cases and mobility, which is heightened when states are closer to each other. This serves as a proof of concept and shows how reducing mobility in more heavily trafficked areas can be more effective.

Optimization of hyperthermia process applied to cancer treatment using multi-objective optimization differential evolution.

Due to the number of cancer cases diagnosed each year and the fatality rate resulting from some more severe types, the improvement of less invasive and more efficient treatment techniques is of great importance. In this context, hyperthermia is a medical procedure in which the tumor region is heated by using an applicator for a certain period, aiming to destroy pathological cells. Computational models can be used to simulate the heating effect of tumors and adjacent cells. In general, the solution to an optimization problem considering factors such as heating temperature, applicator position, and the time in which the region will be subjected to heating can provide important information about the procedure. Traditionally, this type of problem has been addressed in a single objective context, focusing on minimizing the destruction of adjacent healthy tissue considering the area of the applicator constant. Our fundamental objective is to propose a multi-objective design problem considering the minimization of the area subject to the procedure and the time required for the process of hyperthermia in a breast cancer treatment. The problem is constrained by the degree of tissue destruction and by a partial differential equation that describes the phenomenon of heat transfer in both healthy and tumor tissues. The results obtained demonstrate that a point with a good compromise between the objectives can be chosen in such a way that a particular strategy can be defined for each patient.

Sequential time-window learning with approximate Bayesian computation: an application to epidemic forecasting.

The long duration of the COVID-19 pandemic allowed for multiple bursts in the infection and death rates, the so-called epidemic waves. This complex behavior is no longer tractable by simple compartmental model and requires more sophisticated mathematical techniques for analyzing epidemic data and generating reliable forecasts. In this work, we propose a framework for analyzing complex dynamical systems by dividing the data in consecutive time-windows to be separately analyzed. We fit parameters for each time-window through an approximate Bayesian computation (ABC) algorithm, and the posterior distribution of parameters obtained for one window is used as the prior distribution for the next window. This Bayesian learning approach is tested with data on COVID-19 cases in multiple countries and is shown to improve ABC performance and to produce good short-term forecasting. Supplementary Information: The online version contains supplementary material available at 10.1007/s11071-022-07865-x.

Framework for enhancing the estimation of model parameters for data with a high level of uncertainty.

Reliable data are essential to obtain adequate simulations for forecasting the dynamics of epidemics. In this context, several political, economic, and social factors may cause inconsistencies in the reported data, which reflect the capacity for realistic simulations and predictions. In the case of COVID-19, for example, such uncertainties are mainly motivated by large-scale underreporting of cases due to reduced testing capacity in some locations. In order to mitigate the effects of noise in the data used to estimate parameters of models, we propose strategies capable of improving the ability to predict the spread of the diseases. Using a compartmental model in a COVID-19 study case, we show that the regularization of data by means of Gaussian process regression can reduce the variability of successive forecasts, improving predictive ability. We also present the advantages of adopting parameters of compartmental models that vary over time, in detriment to the usual approach with constant values.

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.

Impacts of a delayed and slow-paced vaccination on cases and deaths during the COVID-19 pandemic: a modelling study.

In Brazil, vaccination has always cut across party political and ideological lines, which has delayed its start and brought the whole process into disrepute. Such divergences put the immunization of the population in the background and create additional hurdles beyond the pandemic, mistrust and scepticism over vaccines. We conduct a mathematical modelling study to analyse the impacts of late vaccination along with slowly increasing coverage, as well as how harmful it would be if part of the population refused to get vaccinated or missed the second dose. We analyse data from confirmed cases, deaths and vaccination in the state of Rio de Janeiro in the period between 10 March 2020 and 27 October 2021. We estimate that if the start of vaccination had been 30 days earlier, combined with efforts to drive vaccination rates up, about 31 657 deaths could have been avoided. In addition, the slow pace of vaccination and the low demand for the second dose could cause a resurgence of cases as early as 2022. Even when reaching the expected vaccination coverage for the first dose, it is still challenging to increase adherence to the second dose and maintain a high vaccination rate to avoid new outbreaks.

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.