A model and predictions for COVID-19 considering population behavior and vaccination

Abstract

The effect of vaccination coupled with the behavioral response of the population is not well understood. Our model incorporates two important dynamically varying population behaviors: level of caution and sense of safety. Level of caution increases with infectious cases, while an increasing sense of safety with increased vaccination lowers precautions. Our model accurately reproduces the complete time history of COVID-19 infections for various regions of the United States. We propose a parameter [Formula: see text] as a direct measure of a population's caution against an infectious disease that can be obtained from the infectious cases. The model provides quantitative measures of highest disease transmission rate, effective transmission rate, and cautionary behavior. We predict future COVID-19 trends in the United States accounting for vaccine rollout and behavior. Although a high rate of vaccination is critical to quickly ending the pandemic, a return towards pre-pandemic social behavior due to increased sense of safety during vaccine deployment can cause an alarming surge in infections. Our results predict that at the current rate of vaccination, the new infection cases for COVID-19 in the United States will approach zero by August 2021. This model can be used for other regions and for future epidemics and pandemics.

Figure 1

Results of our behavioral model’s fit to COVID-19 data across six populations in the United States. (a) Shows M representing the ratio of actual infectious cases to reported cases. Reported new infection case data versus model fit for (b) Massachusetts, (c) Florida, (d) South Dakota, (e) California, (f) New York City, and (g) Atlanta. Gray bars represent the daily reports of new COVID-19 cases. The dashed brown lines are the corresponding 7-day average. Our model’s predictions for reported daily cases are shown as the solid red lines.

Figure 2

(a) Level of caution factor $d_I$ and (b) disease transmission rate $\beta$ over the course of COVID-19 in six populations across the United States.

Figure 3

Effect of (a) sense of caution factor, $d_I$, and (b) sense of safety factor, $d_V$ on pandemic trajectory. The dashed blue bar represents the introduction of a vaccine with 95% effectiveness, at a fixed rate of 0.3% of the population per day. Extreme values of $d_I$ represent the extremes of social behavior: the most responsive (black dotted) and the least (red). Sensitivity analysis in (a) considered a fixed sense of safety $d_V=0$, and in (b) considered a fixed level of caution $d_I=500$.

Figure 4

Impact of vaccination rate, $\alpha$, with two social responses to the vaccine. The population in (a) shows no changes in behavior in response to the vaccine, while the population in (b) relaxes its preventative measures as the vaccine is distributed.

Figure 5

Contour plot of the sense of normalcy, $d_V$, and vaccination rate, $\alpha$, versus the total infections since the start of vaccination (red values shown as proportion of the total population). Shown for a high level of caution case ($d_I$ = 500). The pink box shows a possibility of increasing number of total infected cases with increasing vaccination rate at very high sense of safety, and the teal box shows that once the vaccination rate crosses a threshold, the total number of infection cases drop with vaccination rate even at a very high sense of safety.

Figure 6

Results for certain fractions of the population remaining unvaccinated. The entire COVID-19 case history and future predictions are shown in terms of estimated actual new infection cases for California as a representative example. Gray bars represent the daily reports of new COVID-19 cases. The dashed brown lines are the corresponding 7-day average. Our model predictions for the entire duration are also shown as green, gray and yellow curves.

Figure 7

(a) SIRDV compartment model with susceptible (S), vaccinated (V), infectious (I), recovered (R), and deceased (D) populations. Flow between between compartments is shown with arrows. (b) Description of model parameters. (c) and (d) Show variations in disease transmission rate $\beta$, due to social response to infectious and vaccinated populations. (c) $\beta$ for a range of level of caution factor $d_I$ (100, 200, 400), and (d) $\beta$ for a range of sense of safety factor $d_V$ (1, 2, 4).