RESUMEN
This paper considers a nonlinear dynamical model of an ecosystem, which has been established through combining the classical Lotka-Volterra model with the classic SIR model. This nonlinear system consists of a generalist predator that subsists on two prey species in which disease is becoming endemic in one of them. The dynamical analysis methods prove that the system has a chaotic attractor and extreme multistability behavior, where there are infinitely many attractors that coexist under certain conditions. The occurrence of extreme multistability demonstrates the high sensitivity of the system for the initial conditions, which means that tiny changes in the original prey species could enlarge and be widespread, and that could confirm through studying the complexity of the time series of the system's variables. Simulation results of the sample entropy algorithm show that the changes in the system's variables expand over time. It is reasonable now to consider the endemic in the prey species of the system could evolve to be pandemic such as COVID-19. Consequently, our results could provide a foresight about the unpredictability of the COVID-19 outbreak in its original host species as well as after the transmission to other species such as humans.
RESUMEN
A knowledge-based cybernetic framework model representing the dynamics of SARS-CoV-2 inside the human body has been studied analytically and in silico to explore the pathophysiologic regulations. The following modeling methodology was developed as a platform to introduce a predictive tool supporting a therapeutic approach to Covid-19 disease. A time-dependent nonlinear system of ordinary differential equations model was constructed involving type-I cells, type-II cells, SARS-CoV-2 virus, inflammatory mediators, interleukins along with host pulmonary gas exchange rate, thermostat control, and mean pressure difference. This formalism introduced about 17 unknown parameters. Estimating these unknown parameters requires a mathematical association with the in vivo sparse data and the dynamic sensitivities of the model. The cybernetic model can simulate a dynamic response to the reduced pulmonary alveolar gas exchange rate, thermostat control, and mean pressure difference under a very critical condition based on equilibrium (steady state) values of the inflammatory mediators and system parameters. In silico analysis of the current cybernetical approach with system dynamical modeling can provide an intellectual framework to help experimentalists identify more active therapeutic approaches.