Estimating the Resultant Efficacy of the Rollout of Multiple Vaccines in a Population
Hanna Rhae Lyssa Improso (a), Rachelle Sambayan (a), Ma. Cristina Bargo (a), Jose Ernie Lope (a)

(a) Institute of Mathematics, University of the Philippines Diliman

Abstract

A modified SEIR model with vaccination is employed to model the scenario when different vaccine brands with different efficacy rates were administered to the subsets of the population. The resultant efficacy rate of the different vaccines is determined and then used to estimate the fraction of the population that needs to be vaccinated to attain herd immunity. The population is compartmentalized based on the administered vaccine brand and the SEIR model with vaccination is implemented on each of the compartments under the assumption that members of the different compartments can freely interact with each other. To obtain an estimate of the resultant vaccine efficacy, the total infected individuals of the different compartments are compared to that of an uncompartmentalized population with a single vaccine whose efficacy is yet to be estimated. Various scenarios are explored by varying the number of compartments, initial conditions, and vaccine rollout rates, and the resultant efficacy is computed by minimizing the residual sum of squares of the number of infected individuals over a certain period. The results suggest a formula for the resultant vaccine efficacy in terms of the population of the compartments but independent of the vaccine rollout rates.

Keywords: COVID-19 pandemic, SEIR model with vaccination, vaccine efficacy

Topic: Mathematics