Covid-19 Vaccination Strategy Using SIR Epidemic Model
One of the most current issues these days is that of creating and distributing a covid-19 vaccine. Ideally, governments across the globe would vaccinate all of their citizens free of cost. Unfortunately, some countries lack the distribution systems, coordination, or resources to provide this for every person. The question that remains is how should vaccines for covid-19 be used and distributed in a way that is most effective for the entirety of the population? The paper cited below, “Pulse Vaccination Strategy in the SIR Epidemic Model”, investigates this very question using the SIR model. The paper asserts that a “pulse model” for vaccination can be used to eradicate diseases in populations while using less vaccination doses overall. This paper used data collected from pulse measles vaccinations in the 1990’s and constructed an SIR model. Using the SIR model, the experimenters defined a proportion of the susceptible (S) population p that receives the vaccination and this proportion of the susceptible population is vaccinated every t years. There is a maximum value t_max which the experimenters want to determine. Waiting the maximum time between vaccination pulses, t_max, is good because then the least amount of resources are used. However, if the time between pulses exceeds t_max, the entire vaccination scheme would collapse.
This paper is connected closely to the SIR model that was discussed in class. Essentially, the experimenters defined the values for the susceptible population (S), infected population (I), and recovered populations (R) as functions of t (time in years between pulses). The outputs are normalized such that the entire population is represented by 1 or 100%:
S(t) + I(t) + R(t) = 1
The experimenters define these functions using the various population data collected throughout the years. The first derivatives of these functions were then taken and parameters for pulse vaccination were determined.
dS/dt = m – (BI + m)S
dI/dt = BIS – (m + g)I
dR/dt = gI – mR
The parameters were chosen such that the function I(t), the infected population, was constantly decreasing. In theory, the chosen parameters are then applied to the pulse vaccination scheme and thus the number of infected individuals will decrease over time.
This paper’s findings are incredibly interesting and useful, especially given the current circumstances. By applying certain aspects of the SIR model, the covid-19 vaccine could be distributed in a way that minimizes the infected population while saving the most resources possible. However, issues were identified by the experimenters using the SIR model. One big issue is that the assumptions of the SIR model are often too idealistic to apply to a real world population. Another, further issue I have with this article is that the models were fit to and applied to populations dealing with measles and sometimes rubella. These diseases differ greatly from covid-19 in terms of transmission, symptoms, and recovery period. Thus, more research would have to be done in order to apply the findings of this paper to the current covid-19 pandemic.
The research and parameters required to apply the findings of this study to the covid-19 pandemic seem simple initially. Researchers need to determine the proportion of the population to actually vaccinate (p) and the value t for the years in between each vaccination pulse. The issue is that this pandemic is currently an issue and if there is any error with the calculation of p and t, a potentially unsafe vaccination scheme could be put into place with no countermeasure. The vaccination scheme that is most likely to be used by many countries is the mandatory, mass vaccination scheme in which authorities will try to vaccinate as many people as possible. This is the most safe but least efficient method of vaccination for a population. Safety being the primary concern, it is unfortunately unlikely that many nations adopt the pulse vaccination strategy. Thus, many areas of research are available to build on and improve SIR models for vaccination and the viability of pulse vaccinations schemes.
Reference:
Agur, Z.., et al. “Pulse Vaccination Strategy in the SIR Epidemic Model.” Bulletin of Mathematical Biology, Springer-Verlag, 1 Jan. 1985, link.springer.com/article/10.1006/S0092-8240(98)90005-2.