Quantum Mechanics for Population Dynamics

A New Approach to Population Dynamics, A Study of Immigration, Emigration and Fission via Quantum Mechanics

Abstract

A standard single species immigration, emigration and fission ordinary differential equation (ODE) model is derived from a quantum mechanics approach. The stochasticity introduced via quantum mechanics is very different than that of the standard approaches such as demographic stochasticity in the state variables or environmental stochasticity as in uncertainty quantification. This approach yields a standard ODE and predicts the effects of quantum tunneling of probabilities. This approach is explained in such a way that epidemiologists, mathematicians, mathematical biologists, etc who are not familiar with quantum mechanics can understand the methods described here and apply them to more sophisticated situations. The two main results of this approach are (i) standard macroscopic ODE models can be derived from first principles of quantum mechanics instead of making macroscopic heuristic assumptions and (ii) high impact events with low probability of occurrence can be explicitly calculated.