Stochastic Model of Brucellosis in Indian Dairy Herds

A dynamic age-structured stochastic compartmental model incorporating dairy herd demographics was written in R [22 ] to capture transmission of B. abortus within and between dairy herds. As the model is used to capture dynamics in dairy herds typical of Punjab State of India, large ruminants (cows/buffalo) are the only species considered as very few farms or households in this area keep small ruminants (2%) [13 (link)]. In addition, B. abortus is the only species to be isolated from large ruminants here [13 (link)]. Cows and buffalo are assumed to mix homogeneously within the herd as management practices in Punjab are very similar and farms often keep a mixture of both species. Transition between compartments follows a Poisson process using the event-driven Gillespie stochastic simulation algorithm (SSA) implemented using the R package GillespieSSA [23 ]. The model tracks the numbers of livestock in each state; susceptible (S_i), infected (E_i), vaccinated (V_i) (all age groups) and infectious (I_i; adults only), as well as vaccine doses and the number of animals ‘removed’ from the dairy herds when implementing test and removal strategies (figure 1 and electronic supplementary material).
Figure 1.

Model schematic showing the transition between different compartments, where NS(t)=∑ j=3 j=11Sj(t), NE(t)=∑ j=3 j=11Ej(t) and NV(t)=∑ j=3 j=11Vj(t) denote, respectively, the total number of susceptible, exposed and vaccinated adults in the herd; λ, θ, α₁ and ω denote, respectively, the calving rate, probability of vertical transmission, removal rate of newborns and probability a calf is vaccinated and becomes immune; γ is the transition rate between age groups (1 year); β is the effective contact rate; ε_j, P, φ, μ and α_j are the number of new purchases (ε_j, j = 4), the probability that a purchased animal is infected (P) and vaccinated (φ), the rate of loss of infectiousness (μ) and the rate of removal of adults (α_j).