Optimal Vaccination Policy to Prevent Endemicity: A Stochastic Model

TL;DR

This paper models how recurrent vaccination and waning immunity influence the establishment of endemic disease, providing strategies for effective vaccination policies to prevent endemicity.

Contribution

It introduces a stochastic individual-based model incorporating memory effects and derives conditions for endemic equilibrium, highlighting optimal booster scheduling and equitable vaccine distribution.

Findings

Evenly spaced booster doses are more effective than irregular schedules.

A critical vaccination threshold is derived for disease eradication.

Fair vaccine allocation optimally prevents endemicity.

Abstract

We examine here the effects of recurrent vaccination and waning immunity on the establishment of an endemic equilibrium in a population. An individual-based model that incorporates memory effects for transmission rate during infection and subsequent immunity is introduced, considering stochasticity at the individual level. By letting the population size going to infinity, we derive a set of equations describing the large scale behavior of the epidemic. The analysis of the model's equilibria reveals a criterion for the existence of an endemic equilibrium, which depends on the rate of immunity loss and the distribution of time between booster doses. The outcome of a vaccination policy in this context is influenced by the efficiency of the vaccine in blocking transmissions and the distribution pattern of booster doses within the population. Strategies with evenly spaced booster shots at the individual level prove to be more effective in preventing disease spread compared to irregularly spaced boosters, as longer intervals without vaccination increase susceptibility and facilitate more efficient disease transmission. We provide an expression for the critical fraction of the population required to adhere to the vaccination policy in order to eradicate the disease, that resembles a well-known threshold for preventing an outbreak with an imperfect vaccine. We also investigate the consequences of unequal vaccine access in a population and prove that, under reasonable assumptions, fair vaccine allocation is the optimal strategy to prevent endemicity.