**11. Quarantine**

class is practically not feasible and more so, in economically backward countries. Therefore, the critical fraction or proportion of population that needs to be vaccinated is to be determined. Moreover, desired degree of success may not be always obtained due to vaccination because of less than optimum coverage, irregularities in the supply of vaccines, use of low-efficiency vaccines or waning rate of vaccines. All these may lead to re-emergence of disease outbreak, sometimes with increased intensity, owing to the resurgence of the susceptible class finally

Vaccination coverage depends on the characteristics of the endemic equilibrium. At equilibri‐ um, the replacement number, R is equal to the product of basic reproduction ratio and the proportion of susceptibles i.e. R=R0*s*\*. The replacement number is defined as the average number of secondary infections produced by a typical infective during its entire course of infectiousness. Vaccination coverage of *p* reduces the proportion of susceptible to 1-*p*. Higher the magnitude of R0, higher is the vaccination coverage and is complicated by parameter such as vaccine efficacy. Therefore, for disease eradication to occur, R=R0*s*\*(1-*p*) < 1 or *p* > 1-1/ R0. The critical vaccination coverage is expressed by the formula, *pc=*1-1/ R0 and the value has been found to be 0.94 and 0.86 respectively for measles and rubella. An increase in the value results in a decrease of the spatial synchrony of disease dynamics. Smallpox has been successfully removed from the face of the earth because it possesses the least critical vaccination coverage. Vaccine efficacy of 0.97 represents that 3% of those vaccinated do not become immune.

Optimal vaccination coverage and frequency of pulse vaccination has been studied with the help of Pythagore theorem [6]. The important terminologies associated with vaccination has

**Parameters Description**

achievable by vaccinating a proportion of the population

introduced into a population in which a proportion has

eradication by maintaining Basic reproduction number

is a threshold quantity above which levels of infection will

and creating immune individuals

under vaccination equal to one

be high and vaccination fails

been vaccinated

Herd immunity Immunity and protection of the entire community

Basic reproduction number under vaccination Number of secondary cases caused by one primary case

Critical vaccination proportion Proportion of population to be vaccinated to achieve

Re-infection threshold Occurs during transmission induced by partial immunity. It

Vaccine efficacy Effectiveness of the vaccine to induce immunity Eradication likelihood Determined by effective period of immunity

**Table 2.** Glossary of important parameters related to vaccination

resulting in serious side effects.

196 Trends in Infectious Diseases

been presented in Table 2.

Quarantine refers to intentional or forceful isolation of individuals suffering from diseas‐ es like leprosy, plague, cholera, typhus, yellow fever, smallpox, diphtheria, tuberculosis etc. The ultimate objective of the process is to reduce the average infectious period by isolat‐ ing some infectives, so that they do not transmit the infection. To study the effect of quarantine, a new class Q of quarantined individuals has been included in standard SIS and SIR endemic models. They include those who have been removed and isolated either voluntarily or coercively from the Infectious class. The quarantine reproduction number, R0 depends on the quarantine rate constant which governs the transfer rate out of the Infectious class into the Quarantine class [28].
