- Their reproduction “R” varies by time, location, and distancing measures
- Lowering the “R” value is important for decreasing problems with the health system and having time for vaccines.
- Mortality varies on location and different data will project a different outcome, especially because the consistency of the data varies.


University of Pittsburgh

- 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

- 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

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

The paper describes scenarios where it shows how social distancing could affect the number of people infected. These models were not designed to be accurate in the percentages of cases, especially considering when the paper was published.
- In New York, with social distancing, the R0 value decreased by a factor of 2, although the number of cases would still rise by 10% until mid-April.
- If New York were to not have implemented distancing measures, the number of individuals infected by mid-April would be four times the amount that were infected.
- In California, the R0 was brought to a value close to 1, meaning the pandemic was more controlled with distancing measures. However, infections would still have risen until mid-April.

Uses of SIR to determine the effects of social distancing

If social distancing were stopped in May 2020, a hypothetical date proposed by the paper, the pandemic would reemerge as the peak infection rates would be pushed to a later date.
- The R0 of California would return to its original value and the number of infected cases would be similar to the number if no social distancing was enforced. The peak would simply occur at a later date. 
- In New York, due to the first social distancing measure taken, the number of people infected would have been less than if there were no social distancing.
- The peak number of cases after social distancing were terminated would be less than if no social distancing existed. 


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