The Gompertz function describes global dynamics of many natural processes including growth of normal and malignant tissues. On one hand, the Gompertz function defines a fractal. The fractal structure of time-space is a prerequisite condition for the coupling and Gompertzian growth. On the other hand, the Gompertz function is a probability function. Its derivative is a probability density function. Gompertzian dynamics emerges as a result of the co-existence of at least two antagonistic processes with the complex coupling of their probabilities. This dynamics implicates a coupling between time and space through a linear function of their logarithms. The spatial fractal dimension is a function of both scalar time and the temporal fractal dimension. The Gompertz function reflects the equilibrium between regular states with predictable dynamics and chaotic states with unpredictable dynamics; a fact important for cancer chemoprevention. We conclude that the fractal-stochastic dualism is a universal natural law of biological complexity.
Covid-19 appearance and fast spreading took by surprise the international community. Collaboration between researchers, public health workers and politicians has been established to deal with the epidemic. One important contribution from researchers in epidemiology is the analysis of trends so that both current state and short-term future trends can be carefully evaluated. Gompertz model has shown to correctly describe the dynamics of cumulative confirmed cases, since it is characterized by a decrease in growth rate that is able to show the effect of control measures. Thus, it provides a way to systematically quantify the Covid-19 spreading velocity. Moreover, it allows to carry out short-term predictions and long-term estimations that may facilitate policy decisions and the revision of in-place confinement measures and the development of new protocols. This model has been employed to fit the cumulative cases of Covid-19 from several Chinese provinces and from other countries with a successful containment of the disease. Results show that there are systematic differences in spreading velocity between countries. In countries that are in the initial stages of the Covid-19 outbreak, model predictions provide a reliable picture of its short-term evolution and may permit to unveil some characteristics of the long-term evolution. These predictions can also be generalized to short-term hospital and Intensive Care Units (ICU) requirements, which together with the equivalent predictions on mortality provide key information for health officials.