Epidemic Modeling

West Nile virus model


The West Nile virus (WNV) is an arthropod-borne virus (arbovirus) circulating in a natural transmission cycle between mosquitoes (enzootic vectors) and birds (amplifying hosts). Additionally, mainly horses and humans (dead-end hosts) may be infected by blood-feeding mosquitoes (bridge vectors). We developed an epidemic model for the simulation of the WNV dynamics of birds, horses and humans in the U.S., which we apply to the Minneapolis metropolitan area (Minnesota). The SEIR-type model comprises a total of 19 compartments, that are 4 compartments for mosquitoes and 5 compartments or health states for each of the 3 host species. It is the first WNV model that simulates the seasonal cycle by explicitly considering the environmental temperature. The latter determines model parameters responsible for the population dynamics of the mosquitoes and the extrinsic incubation period. Once initialized, our WNV model runs for the entire period 2002-2009, exclusively forced by environmental temperature. Simulated incidences are mainly determined by host and vector population dynamics, virus transmission and herd immunity, respectively. We adjusted our WNV model to fit monthly totals of reported bird, equine and human cases in the Minneapolis metropolitan area. From this process we estimated that the proportion of actually WNV-induced dead birds reported by the Centers for Disease Control and Prevention is about 0.8%, whereas 7.3% of equine and 10.7% of human cases were reported. This is consistent with referenced expert opinions whereby about 10% of equine and human cases are symptomatic (the other 90% of asymptomatic cases are usually not reported). Despite the restricted completeness of surveillance data and field observations, all major peaks in the observed time series were caught by the simulations. Correlation coefficients between observed and simulated time series were R = 0.75 for dead birds, R = 0.96 for symptomatic equine cases and R = 0.86 for human neuroinvasive cases, respectively.

Time series of observed and simulated human cases in the Minneapolis metropolitan area. Period 2002-2009.

R code


The model was developed using the R statistical computing environment (R Development Core Team, 2010).


Laperriere, V., Brugger, K., and F. Rubel, 2011:
Simulation of the seasonal cycles of bird, equine and human West Nile virus cases.
Prev. Vet. Med., 98 , pp. 99-110.