Population dynamics and economic development

<p style='text-indent:20px;'>This research develops a continuous-time optimal growth model that accounts for population dynamics resembling the historical pattern of the demographic transition. The Ramsey model then becomes able to generate multiple determinate or indeterminate stationary equilibria and explain the process of the transition from a state with high fertility and low income per capita to a state with low fertility and high income per capita. The article also investigates the emergence of damped or persistent cyclical dynamics.</p>

Firms, technology, training and government fiscal policies: An evolutionary approach

<p style='text-indent:20px;'>In this paper we propose and analyze a game theoretical model regarding the dynamical interaction between government fiscal policy choices toward innovation and training (I&amp;T), firm's innovation, and worker's levels of training and education. We discuss four economic scenarios corresponding to strict pure Nash equilibria: the government and I&amp;T poverty trap, the I&amp;T poverty trap, the I&amp;T high premium niche, and the I&amp;T ideal growth. The main novelty of this model is to consider the government as one of the three interacting players in the game that also allow us to analyse the I&amp;T mixed economic scenarios with a unique strictly mixed Nash equilibrium and with I&amp;T evolutionary dynamical cycles.</p>

Dynamics of a stochastic HIV/AIDS model with treatment under regime switching

<p style='text-indent:20px;'>This paper focuses on the spread dynamics of an HIV/AIDS model with multiple stages of infection and treatment, which is disturbed by both white noise and telegraph noise. Switching between different environmental states is governed by Markov chain. Firstly, we prove the existence and uniqueness of the global positive solution. Then we investigate the existence of a unique ergodic stationary distribution by constructing suitable Lyapunov functions with regime switching. Furthermore, sufficient conditions for extinction of the disease are derived. The conditions presented for the existence of stationary distribution improve and generalize the previous results. Finally, numerical examples are given to illustrate our theoretical results.</p>