R0 a new epidemiological tool for measuring livestock disease impact

In epidemiology, basic reproductive number -R0 denotes the average number of secondary cases of infectious diseases that one would generate in a completely susceptible population. This is one of the most valuable ideas that mathematical thinking has brought to epidemic theory. The transmission potential of a disease is measured by R0, i.e., count of the number of secondary cases following the introduction of an infection in susceptible population. However many factors influence the rate- Contact rate of host population, 2. The probability of infection being transmitted during contact and 3. Duration of infectiousness.

The concept of the basic reproduction number assumes that one infective case is introduced into a large susceptible population, so that initial spread of infection can be approximated by branching process where one neglects the decline of the number of susceptible in subsequent generations of the epidemic. In this framework, it is clear that the key parameters is the number of secondary cases generated by the initial case. If this number is ≤1, one will get only minor outbreaks with a probability one of extinction while if this number is >1, then there is positive chance of a large outbreak affecting nearly the total population. R0 is a dimensionless and in epidemiology this expression should refer to quantities with dimension `per unit of time’.

In various conditions, not all contacts will be susceptible to infection, that is, some contacts will be immune, for example due to prior infection which has conferred life-long immunity or as a result of previous immunisation. Hence, not all contacts will become infected and the average number of secondary cases will decrease. This is measured by Effective Reproductive Rate (R) defines the average number of secondary cases per infectious case in a population made up both susceptible and non-susceptible hosts. Hence R= R0 x Y, where Y is the fraction of host population that is infected.

Disease prioritization for policy making and planning.

In developing public health policy and planning for livestock disease outbreaks or vaccination, the R0 can be used as an epidemiological tool in addition to case-fatality rate and economic loss incurred due to infectivity. The organisms which are capable of animal-to-animal transmission will have a far greater impact on the population than the organism which cause a single outbreak of disease without secondary cases. Disease transmitted from animal-to-animal have varying transmission potential depending on the infectivity of agent, rates of contact, of susceptibility of contacts. The combined effect of these is summarized by R0, the basic reproduction number or sometimes R, effective reproductive number, which is the average number of secondary cases produced by a typical case in a given population. When R0 >1, cases increases from one generation to next, and an epidemic ensues. When R0 <1, cases decrease from one generation to next, hence R0=1 is defined as epidemic threshold. Further, the definition of Case fatality rate is the organisms with higher case fatality will have will have greater impact in the event of attack.

Estimation of Herd Immunity

Herd immunity occurs when a significant proportion of population (or the herd) have been vaccinated and this provides the protection for unprotected individuals. The larger the number of animals vaccinated in the population, the lower likelihood that a susceptible animal (unvaccinated) will come into contact with the infection. It is more difficult for diseases to spread between individuals if large numbers are already immune and chain of infection is broken. The herd immunity threshold is the proportion of population that needs to be immune in order for an infectious disease to become stable in the herd or population. If this is reached, for example due to immunisation, then each case leads to single new case and the infection will become stable within the population i.e. R0=1, if the threshold is surpassed, then the HIT (Herd Immunity threshold)=1-1/R0 an important measure used in infectious disease control and immunisation and eradication programs.

Initiation of Elimination or Eradication programs

The terms elimination and eradication are often used synonymously in the epidemiological literature. Both refer to the state of zero prevalence of the infection. But a prevalence of zero may refer to a stable or unstable equilibrium. Here stability refers to the results of an introduction of an infectious case in to the population. If the zero equilibrium is stable then the introduction of one case will at most lead to a small number of generations of secondary cases and therefore to a return to the original prevalence of zero. This situation can ether occur naturally, without special interventions because of low contact rates and probabilities of infection per contact or because of permanent intervention like vaccination programmes which reduces the proportion of susceptible sufficiently such that R0 is less than 1. Such a stable prevalence of zero is called elimination.

If however, the zero prevalence is unstable the introduction of an infectious case will lead to a major epidemic and potentially to a subsequent endemic state, depending on the size of the population and the rate of introduction of new susceptibles. A prevalence of zero would be the result of a time-limited intervention after which R0 is allowed to go back to its original level. Such program is called eradication.

Developing Vaccination programs

R0 can be used to determine the minimum coverage required for elimination or eradication assuming a non-selective program, one has to take in to account the effect of a vaccine on an individual. In general, susceptibility of an individual animal is reduced by certain factors and vaccine can reduce the infectious period and infectivity. We assumes a general distribution function for the susceptibility among the vaccinated animals with fraction r is completely immunized, i.e., susceptibility reduced to zero, "herd immunity threshold" or the critical immunisation threshold" (denoted by q _c ) can be calculated by

q_c= 1-1/ R_o

From this the factor E - vaccine efficacy with Reproduction number 12 and when we factor vaccine efficacy E which is about 97%. We get the vaccine coverage (V_c) by the following formula:

V_c= q_c/E

V_c= (1-1/12)/ 0.97 =0.945

R0 determine the herd immunity threshold and therefore the immunization coverage is required to achieve elimination of an infectious disease. A R0 increases higher immunization coverage is required to achieve the herd immunity.