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A new model that describes the life cycle of mosquitoes of the species Aedes aegypti, main carriers of vector-borne diseases, is proposed. The novelty is to include in the model the coexistence of two independent diffusion processes, one fast which obeys the constitutive Fick's law, the other slow which satisfies the Cattaneo evolution equation. The analysis of the corresponding ODE model shows the overall stability of the Mosquitoes-Free Equilibrium (MFE), together with the local stability of the other equilibrium point admitted by the system. Traveling wave type solutions have been investigated, providing an estimate of the minimal speed for which there are monotone waves that connect the homogeneous equilibria allowed by the system. A special section is dedicated to the analysis of the hyperbolic model obtained neglecting the fast diffusive contribution. This particular case is suitable to describe the biological process as it overcomes the paradox of infinite speed propagation, typical of parabolic systems. Several numerical simulations compare the existing models in the literature with those presented in this discussion, showing that although the generalized model is parabolic, the associated wave velocity admits upper bound represented by the speed of the waves linked to the classic parabolic model present in the published literature, so the presence of a slow flux together with a fast one slows down the speed with which a population spreads. [ABSTRACT FROM AUTHOR]

Under voluntary vaccination, a critical role in shaping the level and trends of vaccine uptake is played by the type and structure of information that is received and used by parents of children eligible for vaccination. In this article we investigate the feedbacks of spatial mobility and the spatial structure of information on vaccination dynamics, by extending to a continuous spatially structured setting existing behavioral epidemiology models for the impact of vaccine adverse events (VAEs) on vaccination choices. We considered the simplest spatial setting, namely classical 'Fickian' diffusion, and focused on the noteworthy case where the infection is absent. This scenario mimics the important case of a population where a previously endemic vaccine preventable infection was successfully eliminated, but the re-emergence of the disease must be prevented. This is, for example, the case of poliomyelitis in most countries worldwide. In such a situation, the dynamics of VAEs and of the related information arguably become the key determinant of vaccination decision and of collective coverage. In relation to this 'information issue', we compared the effects of three main cases: (i) purely local information, where agents react only to locally occurred events; (ii) a mix of purely local and global, country-wide, information due e.g., to country-wide media and the internet; (iii) a mix of local and non-local information. By representing these different information options through a range of different spatial information kernels, we investigated: the presence and stability of space-homogeneous, nontrivial, behavior-induced equilibria; the existence of bifurcations; the existence of classical and generalized traveling waves; and the effects of awareness campaigns enacted by the Public Health System to sustain vaccine uptake. Finally, we analyzed some analogies and differences between our models and those of the Theory of Innovation Diffusion.