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Relative population growth affects relative prices through the so-called Balassa–Samuelson (BS) mechanism and that in turn impacts PPP. This paper empirically investigates the relationship between the PPP exchange rate and relative population growth in a panel of 80 selected countries. Following the BS hypothesis, this paper argues that relative population growth affects nominal wages that impact price levels and thereby impacts PPP. Using panel cointegration and fully modified ordinary least square (FMOLS), the empirical results show that there is a stable relationship between PPP exchange rate and relative population growth in the long run. These empirical findings suggest that population growth have an important role in exchange rate determination through PPP.

In the present paper, a modeling in the complex space is combined with complex-valued fractional Brownian motion to get some new results in biological systems. The rational of this approach is as follows. Biological dynamics which evolve continuously in time but are not time differentiable, necessarily exhibit random properties. These random features appear also as a result of the randomness of the proper time of biological systems. Usually, this is taken into account by using white noises that is to say fractals of order two. Fractals of order n larger than two are more suitable for increments with large amplitudes, and they may be introduced by using either real-valued fractal noises with long range memory or Brownian motions with independent increments, which are necessarily complex-valued. In the later case, we are then led to describe biological systems in the complex plane. After some background on the complex-valued fractional Brownian motion, we shall deal successively with population growth, information thermodynamics of order n, nonequilibrium phase transition via fractal noises and complexity of Markovian processes via the concept of informational divergence.

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.