[Paper Review] Parametrization Model Motivated from Physical Processes for Studying the Spread of COVID-19 Epidemic

S. Maltezos|arXiv (Cornell University)|Apr 8, 2020

COVID-19 epidemiological studies4 references4 citations

TL;DR

This paper proposes a three-parameter semi-gaussian parametrization model inspired by physical processes to describe the daily reported cases of COVID-19, fitting the data using a non-linear optimization process. The model enables reliable prediction of the epidemic turning point and quantifies key epidemiological parameters, such as mean infection time and disease control effectiveness, with Greece showing superior flattening of the curve due to high isolation (τ) and low transmission (n).

ABSTRACT

The outbreak of the new virus COVID-19, beyond the human health risks and loss, has caused also very serious problems in a wide range of human activities, including the basic and applied scientific research, mainly that concern world wide collaborations. It is desirable to all of us to have the prospect of quickly predicting a turning point in the daily cases curve of the disease. In this work we face the problem of COVID-19 virus disease spreading by aiming mostly to create a reliable mathematical model describing this mechanism for an isolated society, for cities or even for a whole country. Drawing upon similar mechanisms appearing in the particle detector Physics, we concentrated to the so called, semi-gaussian function of n-degree. This approach can provide some very useful advantages in the data analysis of the daily reported cases of the infected people. Applying this model and fitting to the data, reported until the submission of this work, we have determined, among others, the mean infection time for a citizen in the society under study. We also applied and adopted this model to the reported cases in other countries and we have performed useful comparisons and conclusions.

Motivation & Objective

• To develop a flexible, physically motivated mathematical model for predicting the turning point in daily reported COVID-19 cases.
• To quantify key epidemiological parameters such as mean infection time and reproductive number using real-world data.
• To evaluate the effectiveness of public health policies across countries by comparing the shape and peak suppression of daily case curves.
• To provide a simple yet robust parametrization model adaptable to isolated regions or countries with limited data.
• To introduce a dimensionless figure-of-merit (pr) to assess the success of disease control relative to a reference country (Greece).

Proposed method

• The model uses a three-parameter semi-gaussian function: c(t) = A·t^n·e^(-t/τ), where A is amplitude, n is the degree, and τ is the mean infection time.
• The function is fitted to real daily case data via non-linear optimization, enabling curve fitting to the epidemic's growth and decline phases.
• The model draws analogies from particle detector physics and RC circuit response, leveraging the memoryless property of exponential distributions.
• The parameter n is interpreted as a proxy for population mobility or transportation intensity, while τ reflects isolation effectiveness.
• A dimensionless figure-of-merit, pr = pi/p1, is defined to compare disease control performance relative to Greece (reference, pr = 1).
• The model is applied to data from Greece, China, South Korea, Italy, Switzerland, and the UK, enabling cross-country comparisons.

Experimental results

Research questions

• RQ1 Can a physics-inspired semi-gaussian model accurately predict the turning point in daily reported COVID-19 cases?
• RQ2 How do the model parameters n and τ relate to real-world public health behaviors such as population mobility and isolation measures?
• RQ3 To what extent can the dimensionless figure-of-merit pr quantify the success of national disease control policies?
• RQ4 What is the relationship between the shape of the daily case curve and the effectiveness of public health interventions across different countries?
• RQ5 Can the model reliably estimate the mean infection time (τ) and peak suppression (pr) even with limited or pre-turning-point data?

Key findings

• The model successfully fitted daily case data for Greece, China, South Korea, Italy, Switzerland, and the UK, with reliable parameter estimation in all cases.
• For Greece, the model estimated a mean infection time τ = 6 days, with a peak suppression ratio pr = 1.0, indicating optimal control among the studied countries.
• Italy showed high n = 4.5 and low τ = 5.5 days, indicating high population mobility and less effective isolation, resulting in pr = 1.43.
• South Korea had the highest pr value (4.35), indicating the most effective flattening of the curve, attributed to strong early interventions.
• China had pr = 2.43, reflecting effective control but less optimal than South Korea, with τ = 6.5 days and n = 3.5.
• The model demonstrated that pr decreases by approximately 5% for every 10% increase in n and by 15% for every 10% increase in τ, indicating τ has a stronger impact on curve flattening.