**8.1. Significance of basic reproduction ratio**

susceptible population. If the spreading rate is too low and R0 cannot cross beyond the threshold level, it is not feasible to affect a finite proportion of population and disease dies out in a finite time. In a contact network model, the disease cannot replenish itself and ultimately dies out after a finite number of waves, if R0< 1 with probability 1. Disease persists with positive probability, at least by infecting one person in each wave, if R0 > 1. Keeping and maintaining the value of R0 < 1 reflects the stability of the disease-free equilibrium and creates a condition for clearing of pathogen from the population and thus it is the goal of any public health initiative designed for containment or control of infection. Moreover, the estimation of R0 plays a crucial role in understanding the outbreak and potential danger from emerging infectious disease. The concept of R0 has also been developed for complex models like stochastic and finite systems, models with spatial structure and also macroparasite infections. Comparison of R0 values, based either on their numerical values or area under the infectiousness curve, helps in estimation of relative intrinsic transmissibility of the pathogens [9], [10], [21], [22].

There are also alternative approaches of estimating R0 from available incidence or epidemio‐ logical data which require simplifying assumptions for numerical estimation of some un‐ known parameters. It is assumed that the host population is homogeneous, mixes uniformly and is of constant size in a constant state. The number of contacts per infective is independent of the number of infectives. Infectivity and mortality do not depend on age, genetic make-up, geography. Moreover, it is assumed that all individuals are born susceptible and as soon as disease is acquired, they are no longer considered susceptible. Spreading pattern of the epidemics is controlled by the generation time-scale. All these assumptions may never be fully realized in a practical clinical setting. R0 can be expressed as the ratio of the life expectancy and mean age of acquiring the infection. Thus, higher the R0, lower is the mean age at infection. Another important relationship that can be derived is that the mean age at infection is the reciprocal of the force of infection. A key parameter, the coefficient of transmission for airborne diseases, can be determined from the value of the force of infection. Alternatively, R0 can be estimated from the intrinsic growth rate of the infected class, which is highly dependent on collecting accurate data. Stochastic fluctuations can affect the value of growth rate. In case of vector-borne disease like dengue, R0 was calculated from the survival function, assuming spatial compartments of varying vector density. For multiple classes of infectives, R0 can be

From sensitivity analysis, it has been found that different infection-and population-related factors may affect R0 like, transmission rate, vector mortality, incubation period of the vector,

For both measles and whooping cough in England and Wales from 1945 to 1965, R0 has been found to be nearly 17. For the H1N1 epidemic in UK, R0 has been estimated to be 1.4. Estimation of R0 for SARS by different groups have mostly given the values in the range of 2-4, although a wide range of 1-7 has also been found in the literature. For smallpox, the R0 was found to be in the range of 4< R0 <10. Though an upper bound has been found for pandemic influenza, no lower bound could be obtained. For AIDS, R0 is always greater than 1, especially in African countries and it depends highly on the sexual behavior. For

defined per infection cycle [6], [10], [21].

192 Trends in Infectious Diseases

the relative infectiousness after isolation [21].

The magnitude of R0, along with the disease generation time, help in assessing the time scale of infection, implementing sustainable control measures at the most appropriate time and justifying implementation of costly approaches in management of infectious diseases. Low value of R0 for any infection suggests that the epidemic can be controlled, either by adopting single or combined putative containment procedures [21], [22].

Condition for endemicity can be deduced from an idea of R0. Disease is said to exist in an endemic state when it persists in the population at a low and constant level of prevalence, for which there should be a continuous supply of susceptibles. This happens if deaths and births occur at equal constant rates keeping the population turnover rate at a fixed value. An outcome of this assumption is the negative exponential distribution of age. At endemic equilibrium, the relationship between the proportion of susceptible in the population and the basic reproduc‐ tion ratio is inverse [6].

Though R0 is the widely accepted and used indicator of control measure, it has been observed that different control approaches may produce same degree of reduction of R0 but not same effect on the growth rate. Factors such as timing of secondary infections, negative impact of control measures on the population are not considered while implementing public health initiatives based on the basic reproduction ratio [21].
