Attainment of Herd Immunity: Mathematical Modelling of Survival Rate

TL;DR

This paper uses mathematical modeling and simulations to analyze how the speed of achieving herd immunity affects vulnerable populations, revealing that slower attainment may reduce fatalities but involves complex trade-offs.

Contribution

It generalizes the SIR model by differentiating vulnerable and resilient groups, providing new insights into the impact of herd immunity progress rate on vulnerable populations.

Findings

Slower herd immunity attainment reduces fatalities among vulnerables.

Differentiating populations reveals complex dependence on immunity progress rate.

Quantitative analysis of human cost during epidemic spread.

Abstract

We study the influence of the rate of the attainment of herd immunity (HI), in the absence of an approved vaccine, on the vulnerable population. We essentially ask the question: how hard the evolution towards the desired herd immunity could be on the life of the vulnerables? We employ mathematical modelling (chemical network theory) and cellular automata based computer simulations to study the human cost of an epidemic spread and an effective strategy to introduce HI. Implementation of different strategies to counter the spread of the disease requires a certain degree of quantitative understanding of the time dependence of the outcome. In this paper, our main objective is to gather understanding of the dependence of outcome on the rate of progress of HI. We generalize the celebrated SIR model (Susceptible-Infected-Removed) by compartmentalizing the susceptible population into two categories- (i) vulnerables and (ii) resilients, and study dynamical evolution of the disease progression. We achieve such a classification by employing different rates of recovery of vulnerables vis-a-vis resilients. We obtain the relative fatality of these two sub-categories as a function of the percentages of the vulnerable and resilient population, and the complex dependence on the rate of attainment of herd immunity. Our results quantify the adverse effects on the recovery rates of vulnerables in the course of attaining the herd immunity. We find the important result that a slower attainment of the HI is relatively less fatal. However, a slower progress towards HI could be complicated by many intervening factors.