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Edited and reviewed by: Marc Jean Struelens, Université libre de Bruxelles, Belgium

This article was submitted to Infectious Diseases - Surveillance, Prevention and Treatment, a section of the journal Frontiers in Public Health

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

In a paper published April 26, 2020, researchers predicted the number of cases and deaths would exceed 60,000 in the United States by July: “We estimate that through the end of July, there will be 60,308 (34,063–140,381) deaths from COVID-19 in the USA….” (

This illustrates one problem with existing models. Estimation turns out to be a hard problem due to missing factors that account for all impacts in the models. “Each model makes different assumptions about properties of the novel coronavirus, such as how infectious it is and the rate at which people die once infected. They also use different types of math behind the scenes to make their projections. And perhaps most importantly, they make different assumptions about the amount of contact we should expect between people in the near future (

We claim that the problem of estimating size and duration extends beyond assumptions about properties of the disease and infectiousness. In addition to the limitations expressed above, population, population density, social network topology, and public sentiment impact the rate and size of the spread of a disease. Mathematical models based solely on properties of the disease are likely to fail, while models based on curve fitting of data and social network theory and public sentiment are more likely to succeed. However, these models failed to accurately predict the size and duration of the COVID-19 pandemic due to a number of technical, social, and public policy issues.

Most models assume a uniformly distributed population with the same levels of immunity or susceptibility to infection, and a relatively immobile population. On the contrary, the modern world violates all of these conditions: populations are clustered, people of different age and economic conditions have different susceptibilities to disease, public opinion as to the dangers of a contagion shift over time, and modern people are extremely mobile.

Classical models have proven to be inadequate, largely due to a narrow focus on one or more factors rather than on a broad spectrum of factors.

An example that illustrates the difficulty of making long-range predictions is found in

Generally, models can be separated into categories. For example, perhaps the largest category is regression modeling, whereby data are used to fit a logistics function using OLS (Optimal Least Squares). A suitable parameterized function is selected, and its parameters estimated by OLS curve-fitting. In

In

Alternatively, non-curve-fitting techniques appear to yield comparable results without OLS curve-fitting. In

Finally,

This sampling of alternate models of epidemic spreading illustrates the need for more investigations of epidemic and pandemic models. Models should go beyond traditional curve-fitting and parameter estimating. They need to consider a wider array of factors beyond infection rate and mortality rate. And they need to incorporate the possibility of multiple surges leading to subsequent waves as experienced by the covid-19 pandemic.

TL provided introduction and general content. WA provided details on each article. All authors contributed to the article and approved the submitted version.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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