Effect of demographic and seasonal variability on an influenza epidemic in a metapopulation model

Meteorological factors such as temperature and humidity significantly affect the transmission efficiency of influenza viruses in temperate regions. School-age children aged 5 to 14 years are more susceptible to influenza A virus infection than other age groups. To reveal the impact of seasonal fluctuations in meteorological factors on the spread of influenza and the role of school-age children in disease transmission, we first develop a metapopulation ordinary differential equation model with the seasonal variation of infection probability upon contacting an infectious individual. The basic reproduction number R₀ is obtained. To incorporate demographic variability, a time-nonhomogeneous Markov chain model is reformulated on the basis of the deterministic model. An analytic estimate for the probability of a disease outbreak, as well as an explicit expression for the mean(variance) of the disease extinction time in the absence of an outbreak, is derived. Finally, in the case where the population is divided into two subgroups based on age: school-age children aged 5 to 14 years and individuals of other age groups, our model is applied to study seasonal outbreaks of influenza A viruses in temperate regions. Numerical simulations suggest that: (i) the probability of a disease outbreak depends on the number of reported and unreported infections introduced for the first time, the timing of introduction, and their age group; (ii) the impact of demographic stochasticity on the final size and time until extinction after a disease outbreak depends mainly on the timing of influenza virus introduction; (iii) regardless of the season in which an unreported infected individual is introduced, timely treatment of infected school-age children can help reduce the likelihood of disease outbreaks and lower the mean final size after an outbreak.