Bayesian estimation of the dynamics of pandemic (H1N1) 2009 influenza transmission in Queensland: A space–time SIR-based model

Background A pandemic strain of influenza A spread rapidly around the world in 2009, now referred to as pandemic (H1N1) 2009. This study aimed to examine the spatiotemporal variation in the transmission rate of pandemic (H1N1) 2009 associated with changes in local socio-environmental conditions from May 7–December 31, 2009, at a postal area level in Queensland, Australia. Method We used the data on laboratory-confirmed H1N1 cases to examine the spatiotemporal dynamics of transmission using a flexible Bayesian, space–time, Susceptible-Infected-Recovered (SIR) modelling approach. The model incorporated parameters describing spatiotemporal variation in H1N1 infection and local socio-environmental factors. Results The weekly transmission rate of pandemic (H1N1) 2009 was negatively associated with the weekly area-mean maximum temperature at a lag of 1 week (LMXT) (posterior mean: −0.341; 95% credible interval (CI): −0.370–−0.311) and the socio-economic index for area (SEIFA) (posterior mean: −0.003; 95% CI: −0.004–−0.001), and was positively associated with the product of LMXT and the weekly area-mean vapour pressure at a lag of 1 week (LVAP) (posterior mean: 0.008; 95% CI: 0.007–0.009). There was substantial spatiotemporal variation in transmission rate of pandemic (H1N1) 2009 across Queensland over the epidemic period. High random effects of estimated transmission rates were apparent in remote areas and some postal areas with higher proportion of indigenous populations and smaller overall populations. Conclusions Local SEIFA and local atmospheric conditions were associated with the transmission rate of pandemic (H1N1) 2009. The more populated regions displayed consistent and synchronized epidemics with low average transmission rates. The less populated regions had high average transmission rates with more variations during the H1N1 epidemic period.

Numerical analysis of a new space-time variable fractional order advection-dispersion equation

Many physical processes appear to exhibit fractional order behavior that may vary with time and/or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. In this paper, we consider a new space–time variable fractional order advection–dispersion equation on a finite domain. The equation is obtained from the standard advection–dispersion equation by replacing the first-order time derivative by Coimbra’s variable fractional derivative of order α(x)∈(0,1]α(x)∈(0,1], and the first-order and second-order space derivatives by the Riemann–Liouville derivatives of order γ(x,t)∈(0,1]γ(x,t)∈(0,1] and β(x,t)∈(1,2]β(x,t)∈(1,2], respectively. We propose an implicit Euler approximation for the equation and investigate the stability and convergence of the approximation. Finally, numerical examples are provided to show that the implicit Euler approximation is computationally efficient.