- Exponential behavior is present at the start of the pandemic because recoveries and deaths are negligible and infections are growing, meaning it is also most effective at the beginning of a pandemic. 
- This data was drawn from Wuhan where patient data shows that hospitalized patients either pass or are discharged between 17 to 21 days.
- In the graph, multiple countries observed exponential growth at the start of the pandemic.
- They estimated exponential growth 15 to 20 days after outbreak with no social distancing isolation or quarantine.
- Death began to exponentially increase as well after initial low counts where there is a delay between the beginning of the pandemic and deaths occurring.


Exponential Growth Model for the COVID-19 Pandemic

- This model is a point process model that models the rate of infection over a period of time and allows for parametric and nonparametric estimates of the reproduction number.
- During this time, the reproduction number begins to change over time due to alterations in the public’s behavior
- Used to estimate extinction in the early stages of the pandemic.
- The data used in this model involved uses mortality numbers.
- They also used available data from California, New York and Indiana, to estimate the reproduction number and identify where they are in the timeline of the pandemic.
- These have been used for other diseases like Ebola and even other social interactions such as gang violence and emails, but it is still underutilized in the epidemiology field. 

Self-Exciting Branching Process Model for the COVID-19 Pandemic

The susceptible exposed infected resistant model is a classic compartmental model where N is the population size. S is the number of people who are susceptible, I is the number of people who have been infected and R is the number of people who are resistant. In the COVID-19 pandemic, due to the small death rate, the number of people who died are also counted as people who are resistant. During the time of this study and the timescale of the model, it was assumed that people who were infected and recovered would not be counted in the susceptible group again.

Susceptible-Infected-Resistance (SIR) Compartment Model

The models were chosen for their simplicity, minimal parameters, and their ability to be specific to a region. The models had varying levels of effectiveness depending on the stage of the pandemic.
- Exponential Growth Model
- Self-Exciting Branching Process Model
- Susceptible-Infected-Resistance (SIR) Compartment Model


Grand Valley State University

- The results were effected when the data was either confirmed cases or mortality data.
- Many other aspects of disease spread were not considered (i.e. incubation time, and asymptomatic individuals) either because the data was not available or because they were not included for parsimony and accessibility


Considerations in Using the Models for the COVID-19 Pandemic

Bertozzi, A. L., Franco, E., Mohler, G., Short, M. B., & Sledge, D. (2020). The challenges of modeling and forecasting the spread of COVID-19. Proceedings of the National Academy of Sciences, 117(29), 16732-16738 https://doi.org/10.1073/pnas.2006520117. 

The challenges of modeling and forecasting the spread of COVID-19

Three Macroscopic Models Presented to Forecast the Spread of COVID-19

- Non-pharmaceutical public health interventions, like social distancing, are important for decreasing the impact of the infections. It won't be impactful unless it is sustained over time.
- These models could be used for funding measures for the economic effects of social distancing and sheltering in place. 
- Only the point process models track the reproductive number over time.


Discussion of Predicting COVID-19 With Models

- These models are simple and they vary for each location. 
- They also have several areas of uncertainty due to the little data available when the paper was published. It was unknown what distancing measure would be taken at the time of writing the paper.
- The variability is difficult for policy makers who need to make the social and economic decisions and understand that lowering the interventions will cause an increase in the prevalence of the disease. 

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