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

Abstract

Background: The COVID-19 pandemic is one of the worst public health crises the world has ever faced. A major hindrance in making apt decisions by health control systems is the fact that protocols tested in other epidemics are no guarantee of success to control the COVID-19 epidemic, given its singular nature and complexity. The occurrence of two or more waves of infections all over the world poses an even greater challenge. An effective way to assist health authorities in adopting public policies to face the COVID-19 pandemic depends on smart analytics and visualization. Purpose: We present the software Modinterv as a tool to monitor, in an automated and user-friendly manner, the evolution and trend of COVID-19 epidemic curves, both for cases and deaths. Methods: The Modinterv software uses parametric generalized growth models, together with machine learning algorithms, to fit epidemic curves with one or two waves of infec- tions of cases and deaths for countries around the world as well as for states and cities in Brazil and the USA. The richness of the implemented models lies in the possibility of detecting the distinct acceleration regimes of the disease in places where there are one or two waves of infections. Results: We show how growth models can be combined with machine learning algorithms in an automated software that can identify the current stage of the COVID-19 epidemic curve in the selected place. 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 the chosen location but also to make short term predictions as to how the curves may evolve.

Multiple waves of COVID-19: A pathway model approach

“…For example, from the fitted theoretical daily curve, it is a simple matter to determine its maxima and minima, where the former points correspond to the waves' peaks, when the epidemic was at its worst periods; while the latter indicate periods when an epidemic wave has subsided, meaning that some control of the disease spread had by then been attained, after which a resurgence of infections takes place (probably owing to relaxation of control measures), thus characterizing the beginning of a new wave. Obtaining reliable estimates for the starting and peak dates for each successive wave is important for researchers and health authorities de Lima Gianfelice It is important to point out that the type of information extracted from mathematical models, such as the PM, cannot be easily obtained-at least not with the same degree of accuracy-from a mere visual inspection of neither the raw empirical data nor its moving-average smoothed version Vasconcelos et al (2022);Brum et al (2022). Indeed, the large fluctuations in the daily data make usual smoothing procedures less reliable for such purposes.…”

“…Having reliable mathematical models and numerical algorithms to describe epidemic curves with multiple waves is therefore an important step in this endeavor. Several models have been considered in the literature to describe COVID-19 curves with multiple waves, such as compartmental Friston et al (2020b,a); Cacciapaglia et al (2020) and growth Vasconcelos et al (2021a); Brum et al (2022) models with with time-dependent parameters, among others. These models, albeit satisfactory in many cases, have the disadvantage that their defining ordinary differential equations (ODE) need to be integrated numerically, which makes fitting the model to empirical data more cumbersome.…”

ModInterv: An automated online software for modeling epidemics

“…If the user chooses to perform the curve fit (by clicking on the appropriate button), the non-linear least square minimization problem is dealt with via the Levenberg-Marquardt algorithm implemented in Python by the LMFIT package [18]. From the best-fit curve, the software then determines the epidemic's previous and current stages in the chosen location by computing certain characteristic dynamical points (zeros of the second to the fourth derivatives) [19] using the SciPy package [20]. While the software's front-end is built using the IPython and IPywidgets frameworks, its back-end is provided by a binder [21] server, which builds a Docker image from an IPython notebook into an interactive executable that can be converted to an HTML file, thus rendering the software accessible for online use.…”

“…Regarding wave detection, the main difficulty lies in finding which of the (many) local maxima and minima detected by the Python's native signal processing module are actually local maxima and minima of the epidemic curve, rather than random fluctuations. In the current version of ModInterv we have implemented a filter based on the relative amplitudes of nearby maxima/minima to reject those that are likely due to fluctuations [19]. We are currently investigating the possibility of using a more selective algorithm recently introduced in the literature for detecting relevant maxima and minima [27].…”

“…Another difficulty stems from the often large number of parameters that need to be determined from the chosen empirical data (there are 7𝑁 − 2 free parameters for an epidemic curve with 𝑁 waves). To avoid overfitting, we have implemented a multi-step procedure in which we begin by fitting the first wave and then successively include data for each subsequent wave, whereby each next partial fit uses the fitted parameters from the previous step as initial guesses [19], until the entire dataset is included. This multi-step routine may, on occasion, render the numerical fit rather time consuming, especially for curves with four or more waves.…”