Estimating the Basic Reproductive Number for COVID-19 using the SIRD model
In class, we discussed two models for the spread of epidemics. One model was the branching process model, which begins with “patient zero” and then spreads through contact networks in several waves, each infected person passing the disease with a probability p to people they have been in contact with. There is also another model known as the SIR model, which adapts the branching process model into a network setting. In this model, each node in the network will go through 3 changing states, susceptible (S), infectious (I), or removed (R). To determine if a disease will persist indefinitely or die out in a finite number of steps, a basic reproductive number R0 can be estimated. In the branching process model, the basic reproductive number is calculated using the product of the probability, p, that a neighbor will contract the disease and the number of neighbors, k, that each node has. This number can always be brought down by trying to decrease the values of p and k. p can be reduced by improving sanitary habits, and k can be reduced by quarantining. These are typically measures people take when trying to stop an epidemic, which was seen in the past months when many states and cities took protective measures.
For the current COVID-19 pandemic, a SIRD model, which is a modified version of the SIR model, has been used to calculate the basic reproductive number. This SIRD model has an additional state: the diseased (D) state. Each state in the SIRD model can be described with a differential equation describing its change. Here are the four equations:
S(t) describes the total susceptible cases throughout time, I(t) describes the infectious cases throughout time, R(t) describes the recovered cases throughout time, and D(t) describes the diseased cases throughout time. These equations include the coefficient of infection α1, the coefficient of recovery α2, and the coefficient of mortality α3, which all need to be used to calculate the basic reproductive number, R0, in the following equation:
The researchers used reported data from multiple countries dating up to July 30, 2020 to find the three coefficients using statistical analysis. They then calculated the basic reproductive number for various countries using the above equation.
The country that had the highest basic reproductive number was The Syrian Arab Republic with an R0 of 2.7936, and the country with the lowest basic reproductive number was Nigeria with an R0 of 1.0011. The researchers were also able to use R0 to predict when we will reach a decrease of infections of COVID-19. For the United States, the predicted dates were August – September. This prediction might have been true for a brief moment, however, once the third wave hit the United States out of nowhere, the cases soared higher than before. A decrease in infections may mislead the reader to make the assumption that infections will never increase again after the stated time period. Therefore, I think the article could have done a better job of communicating that and expanding more on these predictions.
Making these types of predictions with a new disease can be difficult. There are many factors that come into play such as new orders being issued by states and cities, and also the level of enforcement that are placed on these orders. The lack of information regarding this new virus can also make it difficult to create accurate predictions. Back in July, when this research was done, COVID-19 was still new and not much was known about it. However, information evolves, so now more information may be known, especially that regarding how long a recovered individual may be immune before being able to become infected with the virus again. Surely, with new data and information about the virus, the basic reproductive number can become a better tool to create more accurate predictions about when the pandemic will possibly begin to die down.
Source: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7438206/