  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.
