Longitudinal Projection of Herd Prevalence of Influenza A(H1N1)pdm09 Virus Infection in the Norwegian Pig Population by Discrete-Time Markov Chain Modelling

In order to quantify projections of disease burden and to prioritise disease control strategies in the animal population, good mathematical modelling of infectious disease dynamics is required. This article investigates the suitability of discrete-time Markov chain (DTMC) as one such model for forecasting disease burden in the Norwegian pig population after the incursion of influenza A(H1N1)pdm09 virus (H1N1pdm09) in Norwegian pigs in 2009. By the year-end, Norway’s active surveillance further detected 20 positive herds from 54 random pig herds, giving an estimated initial population prevalence of 37% (95% CI 25–52). Since then, Norway’s yearly surveillance of pig herd prevalence has given this study 11 years of data from 2009 to 2020 to work with. Longitudinally, the pig herd prevalence for H1N1pdm09 rose sharply to >40% in three years and then fluctuated narrowly between 48% and 49% for 6 years before declining. This initial longitudinal pattern in herd prevalence from 2009 to 2016 inspired this study to test the steady-state discrete-time Markov chain model in forecasting disease prevalence. With the pig herd as the unit of analysis, the parameters for DTMC came from the initial two years of surveillance data after the outbreak, namely vector prevalence, first herd incidence and recovery rates. The latter two probabilities formed the fixed probability transition matrix for use in a discrete-time Markov chain (DTMC) that is quite similar to another compartmental model, the susceptible–infected–susceptible (SIS) model. These DTMC of predicted prevalence (DTMCP) showed good congruence (Pearson correlation = 0.88) with the subsequently observed herd prevalence for seven years from 2010 to 2016. While the DTMCP converged to the stationary (endemic) state of 48% in 2012, after three time steps, the observed prevalence declined instead from 48% after 2016 to 25% in 2018 before rising to 29% in 2020. A sudden plunge in H1N1pdm09 prevalence amongst Norwegians during the 2016/2017 human flu season may have had a knock-on effect in reducing the force of infection in pig herds in Norway. This paper endeavours to present the discrete-time Markov chain (DTMC) as a feasible but limited tool in forecasting the sequence of a predicted infectious disease’s prevalence after it’s incursion as an exotic disease.