Incorporating the mutational landscape of SARS-COV-2 variants and case-dependent vaccination rates into epidemic models

Abstract

Coronavirus Disease (COVID-19), which began as a small outbreak in Wuhan, China, in December 2019, became a global pandemic within months due to its high transmissibility. In the absence of pharmaceutical treatment, various non-pharmaceutical interventions (NPIs) to contain the spread of COVID-19 brought the entire world to a halt. After almost a year of seemingly returning to normalcy with the world's quickest vaccine development, the emergence of more infectious and vaccine resistant coronavirus variants is bringing the situation back to where it was a year ago. In the light of this new situation, we conducted a study to portray the possible scenarios based on the three key factors: impact of interventions (pharmaceutical and NPIs), vaccination rate, and vaccine efficacy. In our study, we assessed two of the most crucial factors, transmissibility and vaccination rate, in order to reduce the spreading of COVID-19 in a simple but effective manner. In order to incorporate the time-varying mutational landscape of COVID-19 variants, we estimated a weighted transmissibility composed of the proportion of existing strains that naturally vary over time. Additionally, we consider time varying vaccination rates based on the number of daily new cases. Our method for calculating the vaccination rate from past active cases is an effective approach in forecasting probable future scenarios as it actively tracks people's attitudes toward immunization as active case changes. Our simulations show that if a large number of individuals cannot be vaccinated by ensuring high efficacy in a short period of time, adopting NPIs is the best approach to manage disease transmission with the emergence of new vaccine breakthrough and more infectious variants.

Keywords: Break-through variants; Non-pharmaceutical interventions (NPIs); Reinfection; Vaccination rate; Waning immunity.

Fig. 1

SEIR (Susceptible, Exposed, Infected, Recovered) type Compartmental Model. Here, people moves from susceptible (S) and vaccinated (V) compartment to exposed compartment (E and E_v) at $\frac{\beta \sigma }{N}$ and $\frac{\beta \rho \sigma }{N}$ respectively. From E and E_v people become infected (I and I_v) after incubation period α. Then from I and I_v, infected people either go to the recovery compartment R or die. With the waning of antibodies, individuals move back to the S compartment from the R and V compartments.

Fig. 2

(a) Based on CDC's Prevalence statistics, the change in prevalence of variants of coronavirus over time from May 29 to August 28 (Center for Disease Control, 2021a). (b) The relative infectivity of circulating viral variants is shown based on 50% increase in infectivity for alpha (B.1.1.7) with respect to other co-circulating variants and a 50% increase in infectivity for delta (B.1.617.2) in comparison to alpha (B.1.1.7) (blue circles). To estimate future relative infectivity, a log-logistic equation is fitted with the model (brown curve) (See Appendix B).

Fig. 3

(a) Daily data on infections and vaccination rate from the Center for Disease Control (2021a). (b) The brown curve line here represents the log-logistic function which estimates the vaccination rate.

Fig. 4

The effect of NPIs adoption and vaccine efficacy on the daily number of infected cases is depicted in this figure. Figures a, b, and c depict the change in daily case count with fixed vaccine efficacy (70%, 80%, 95%) with changing adoption of NPIs, while figures d, e, and f depict the corresponding cumulative case count. From a, b, c, d, e, f it is clear that if the majority of the population uses NPIs, NPIs will have the greatest influence on lowering the daily number of instances in the short and long term. If NPI adoption is not achievable, the only way to minimize the number of cases is to have a high vaccination rate with high effectiveness (Check out Appendix C for a comparison of peak values.).

Fig. 5

Heat-map here depicts how with fixed vaccine efficiency the effective reproduction number (R_e) varies with vaccination rates and adoption of NPIs. With vaccine efficacy 80%, the most efficient method to halt the spread of the disease is to increase immunization rates paired with good implementation of NPIs until herd immunity is reached.