ModInterv COVID-19: An online platform to monitor the evolution of epidemic curves

We present the software ModInterv as an informatics tool to monitor, in an automated and user-friendly manner, the evolution and trend of COVID-19 epidemic curves, both for cases and deaths. The ModInterv software uses parametric generalized growth models, together with LOWESS regression analysis, to fit epidemic curves with multiple waves of infections for countries around the world as well as for states and cities in Brazil and the USA. The software automatically accesses publicly available COVID-19 databases maintained by the Johns Hopkins University (for countries as well as states and cities in the USA) and the Federal University of Viçosa (for states and cities in Brazil). The richness of the implemented models lies in the possibility of quantitatively and reliably detecting the distinct acceleration regimes of the disease. We describe the backend structure of software as well as its practical use. The software helps the user not only to understand the current stage of the epidemic in a chosen location but also to make short term predictions as to how the curves may evolve. The app is freely available on the internet (http://fisica.ufpr.br/modinterv), thus making a sophisticated mathematical analysis of epidemic data readily accessible to any interested user.

Multiple waves of COVID-19: a pathway model approach.

A generalized pathway model, with time-dependent parameters, is applied to describe the mortality curves of the COVID-19 disease for several countries that exhibit multiple waves of infections. The pathway approach adopted here is formulated explicitly in time, in the sense that the model's growth rate for the number of deaths or infections is written as an explicit function of time, rather than in terms of the cumulative quantity itself. This allows for a direct fit of the model to daily data (new deaths or new cases) without the need of any integration. The model is applied to COVID-19 mortality curves for ten selected countries and found to be in very good agreement with the data for all cases considered. From the fitted theoretical curves for a given location, relevant epidemiological information can be extracted, such as the starting and peak dates for each successive wave. It is argued that obtaining reliable estimates for such characteristic points is important for studying the effectiveness of interventions and the possible negative impact of their relaxation, as it allows for a direct comparison of the time of adoption/relaxation of control measures with the peaks and troughs of the epidemic curve.

ModInterv COVID-19: An online platform to monitor the evolution of epidemic curves.

We present the software ModInterv as an informatics tool to monitor, in an automated and user-friendly manner, the evolution and trend of COVID-19 epidemic curves, both for cases and deaths. The ModInterv software uses parametric generalized growth models, together with LOWESS regression analysis, to fit epidemic curves with multiple waves of infections for countries around the world as well as for states and cities in Brazil and the USA. The software automatically accesses publicly available COVID-19 databases maintained by the Johns Hopkins University (for countries as well as states and cities in the USA) and the Federal University of Viçosa (for states and cities in Brazil). The richness of the implemented models lies in the possibility of quantitatively and reliably detecting the distinct acceleration regimes of the disease. We describe the backend structure of software as well as its practical use. The software helps the user not only to understand the current stage of the epidemic in a chosen location but also to make short term predictions as to how the curves may evolve. The app is freely available on the internet (http://fisica.ufpr.br/modinterv), thus making a sophisticated mathematical analysis of epidemic data readily accessible to any interested user.

ModInterv: An automated online software for modeling epidemics.

The COVID-19 pandemic has proven the importance of mathematical tools to understand the evolution of epidemic outbreaks and provide reliable information to the general public and health authorities. In this perspective, we have developed ModInterv, an online software that applies growth models to monitor the evolution of the COVID-19 epidemic in locations chosen by the user among countries worldwide or states and cities in the USA or Brazil. This paper describes the software capabilities and its use both in recent research works and by technical committees assisting government authorities. Possible applications to other epidemics are also briefly discussed.

Situation of COVID-19 in Brazil in August 2020: An Analysis via Growth Models as Implemented in the ModInterv System for Monitoring the Pandemic

In this work we introduce a novel methodology to classify the dynamical stages of an epidemic, based on the different acceleration regimes of the corresponding growth curve. Our classification scheme is implemented by fitting the empirical data with a general class of mathematical growth models, from which we compute not only the growth acceleration but also its jerk and jounce (i.e., the first and second derivatives of the acceleration, respectively), thus allowing for a finer distinction of the epidemic stages. Using this methodology, we analyze the cumulative curves of deaths attributed to COVID-19 in the 26 Brazilian States and the Federal District, up until August 21, 2020. The online application ModIntervCOVID-19, which automatically implements the classification scheme and which can be accessed via an internet browser or a mobile app, was used to investigate the epidemic stages in each of the Brazilian federal units. The analysis revealed that almost all states in the Northern and Northeastern regions were already in the saturation phase, meaning that the epidemic was relatively under control, whereas in all Southern states and in most states in the Midwest the epidemic was still accelerating or showed only a slight deceleration. The Southeastern region presented a great diversity of epidemic stages, with each state being found at a different stage, ranging from acceleration to saturation. It is argued that understanding this heterogeneous geographical distribution of the epidemic is relevant for public health authorities, as it may help in devising more effective strategies against the COVID-19 pandemic in a continental country like Brazil.

Situation of COVID-19 in Brazil in August 2020: An Analysis via Growth Models as Implemented in the ModInterv System for Monitoring the Pandemic

In this work we introduce a novel methodology to classify the dynamical stages of an epidemic, based on the different acceleration regimes of the corresponding growth curve. Our classification scheme is implemented by fitting the empirical data with a general class of mathematical growth models, from which we compute not only the growth acceleration but also its jerk and jounce (i.e., the first and second derivatives of the acceleration, respectively), thus allowing for a finer distinction of the epidemic stages. Using this methodology, we analyze the cumulative curves of deaths attributed to COVID-19 in the 26 Brazilian States and the Federal District, up until August 21, 2020. The online application ModInterv COVID-19, which automatically implements the classification scheme and which can be accessed via an internet browser or a mobile app, was used to investigate the epidemic stages in each of the Brazilian federal units. The analysis revealed that almost all states in the Northern and Northeastern regions were already in the saturation phase, meaning that the epidemic was relatively under control, whereas in all Southern states and in most states in the Midwest the epidemic was still accelerating or showed only a slight deceleration. The Southeastern region presented a great diversity of epidemic stages, with each state being found at a different stage, ranging from acceleration to saturation. It is argued that understanding this heterogeneous geographical distribution of the epidemic is relevant for public health authorities, as it may help in devising more effective strategies against the COVID-19 pandemic in a continental country like Brazil.

Power law behaviour in the saturation regime of fatality curves of the COVID-19 pandemic.

We apply a versatile growth model, whose growth rate is given by a generalised beta distribution, to describe the complex behaviour of the fatality curves of the COVID-19 disease for several countries in Europe and North America. We show that the COVID-19 epidemic curves not only may present a subexponential early growth but can also exhibit a similar subexponential (power-law) behaviour in the saturation regime. We argue that the power-law exponent of the latter regime, which measures how quickly the curve approaches the plateau, is directly related to control measures, in the sense that the less strict the control, the smaller the exponent and hence the slower the diseases progresses to its end. The power-law saturation uncovered here is an important result, because it signals to policymakers and health authorities that it is important to keep control measures for as long as possible, so as to avoid a slow, power-law ending of the disease. The slower the approach to the plateau, the longer the virus lingers on in the population, and the greater not only the final death toll but also the risk of a resurgence of infections.

Modelling fatality curves of COVID-19 and the effectiveness of intervention strategies.

The main objective of the present article is twofold: first, to model the fatality curves of the COVID-19 disease, as represented by the cumulative number of deaths as a function of time; and second, to use the corresponding mathematical model to study the effectiveness of possible intervention strategies. We applied the Richards growth model (RGM) to the COVID-19 fatality curves from several countries, where we used the data from the Johns Hopkins University database up to May 8, 2020. Countries selected for analysis with the RGM were China, France, Germany, Iran, Italy, South Korea, and Spain. The RGM was shown to describe very well the fatality curves of China, which is in a late stage of the COVID-19 outbreak, as well as of the other above countries, which supposedly are in the middle or towards the end of the outbreak at the time of this writing. We also analysed the case of Brazil, which is in an initial sub-exponential growth regime, and so we used the generalised growth model which is more appropriate for such cases. An analytic formula for the efficiency of intervention strategies within the context of the RGM is derived. Our findings show that there is only a narrow window of opportunity, after the onset of the epidemic, during which effective countermeasures can be taken. We applied our intervention model to the COVID-19 fatality curve of Italy of the outbreak to illustrate the effect of several possible interventions.