Identifiability analysis and parameter estimation of a chikungunya model in a spatially continuous domain

We investigate the identifiability and estimation of parameters of a chikungunya epidemic transmission model. As a novelty, this model incorporates the spatial mobility of humans described as Brownian random motion. Indeed, it is a factor that has influenced the re-emergence of several epidemic diseases. The displacement of mosquitoes is omitted since it is limited to a few meters. This model couples a mosquito dynamics model and a transmission virus model between humans and mosquitoes populations. The mosquito larvae and the human population are supposed to be observed. The complete model is then composed of a reaction-diffusion system coupled with ordinary differential equations (ODEs). The diffusion is assumed to be local. For such a model, the identifiability analysis is studied at first to ensure that the parameters can be uniquely identified. From the identifiability study, we propose a numerical procedure for obtaining a first estimate of the parameters of the transmission virus model without any knowledge of them.