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In this contribution, we present a predictive tool developed to help in the management of the evolution of the COVID-19 pandemic situation in Rio Grande do Sul (RS) - Brazil. This tool is the result of georeferenced data analysis, mathematical modeling, and parameter calibration for the dynamics of a SIR-type model defined on a spatial structure that allows distinct subpopulations to interact, similar to the controlled distancing (A_l for l = 1, ···, 21) groupings proposed by the RS government and public health authorities. The predictive analysis, updated biweekly, provides three distinct scenarios per month (milder, average, and severe) and is made available as WebSIGs (Geographic Information System - GIS). The forecast of the average scenario for each Al group is the result of a simulation of the proposed SIRtype dynamics with calibrated parameters derived from an augmented Lagrangian maximum a posteriori estimation and data on the number of infected cases made available by the RS Health Secretariat. The milder and severe scenarios are obtained from the average scenario, with changes in the contagion rates of each Al group. When compared to the number of infections reported in each Al group, the modeling predictions for a biweekly time window (the first two weeks) were quite satisfactory, with errors ranging from 0% to 5.13%, gradually increasing over time. Therefore, we suggest a biweekly re-calibration of the parameters and corresponding forecasts as a wise strategy.

The current pandemic is a great challenge for several research areas. In addition to virology research, mathematical models and simulations can be a valuable contribution to the understanding of the dynamics of the pandemic and can give recommendations to both physicians and politicians. In this paper we give an overview about mathematical models to describe the pandemic by differential equations. As a matter of principle the historic origin of the epidemic growth models will be remembered. Moreover we discuss models for the actual pandemic of 2020/2021. This will be done based on actual data of people infected with COVID-19 from the European Centre for Disease Prevention and Control (ECDC), input parameters of mathematical models will be determined and applied. These parameters will be estimated for the UK, Italy, Spain, and Germany and used in a SIR-type model. As a basis for the model's calibration, the initial exponential growth phase of the COVID-19 pandemic in the named countries is used. Strategies for the commencing and ending of social and economic shutdown measures are discussed. To respect heterogeneity of the people density in the different federal states of Germany diffusion effects are considered. [ABSTRACT FROM AUTHOR]

The current pandemic is a great challenge for several research areas. In addition to virology research, mathematical models and simulations can be a valuable contribution to the understanding of the dynamics of the pandemic and can give recommendations to physicians and politicians. Based on actual data of people infected with COVID-19 from the European Center for Disease Prevention and Control (ECDC), input parameters of mathematical models will be determined and applied. These parameters will be estimated for the UK, Italy, Spain, and Germany and used in an S I R -type model. As a basis for the model’s calibration, the initial exponential growth phase of the COVID-19 pandemic in the named countries is used. Strategies for the commencing and ending of social and economic shutdown measures are discussed.

Abstract: The aim of this paper is to show in explicit detail that, due to the effects of waning and boosting of immunity, an increasing force of infection does not necessarily lead to an increase in the incidence of disease. Under certain conditions, a decrease of the force of infection may in fact lead to an increase of the incidence of disease. Thus we confirm and reinforce the conclusions from , concerning pertussis. We do so, however, in the context of Campylobacter infections in humans deriving from animal reservoirs. For such an externally ‘driven’ epidemic we can ignore the transmission feedback cycle and treat the force of infection as a parameter. As this parameter is, to a certain extent, under public health control, our findings constitute an important warning: reducing exposure may not necessarily lead to a reduction in the occurrence of clinical illness. In a second part of the paper we relate the model parameters to the available data concerning campylobacteriosis. [Copyright &y& Elsevier]