A Vaccination Model for COVID-19 in South Africa

The COVID-19 virus has spread to all corners of the world leaving researchers with countless questions related to the disease. In the absence of a vaccine, governments mandated protocols such as social distancing, lockdowns, and other related policies to mitigate the spread of the disease. Our Masamu Advanced Study Institute (MASI) subgroup is modeling the ongoing outbreak with a focus on how government policies and widely available vaccines can impact infection dynamics.

We formulated a compartmental system of ordinary differential equations (ODEs) for the disease in South Africa that includes vaccinated classes (see Figure 1). We obtained cumulative case data collected on a weekly basis and related inflection points in the data to government policies to approximate time points where collective behavior (and therefore model parameters) changed.

We used this information along with a least-square optimization scheme to estimate parameters that vary over the course of our simulations (Figure 2).

Using our estimated parameters and resulting simulations in combination with the timing of government policies, we are able to assess the impact of certain non-vaccine intervention strategies (Figure 3 below). Results indicate that collective behavior can be just as effective as widespread vaccination in certain cases.

South Africa is about six months behind the United States with respect to their vaccine rollout. We analyze the impact of widely available vaccines by incorporating what is known about the efficacy of available vaccines to our model to consider how they can alter infection dynamics. See Figure 4 below.