Quantum Mechanics Applied to Susceptible-Infected Model (original) (raw)

Epidemics with a Path to Quantum Epidemics

American Journal of Biomedical Science & Research

Mini Review [5] Insist that the final state of an epidemic terminates when the infection dies after undergoing transitions without producing any new infections, as based on the extended general epidemic

Coarse, Medium or Fine? A Quantum Mechanics Approach to Single Species Population Dynamics

2020

Standard heuristic mathematical models of population dynamics are often constructed using ordinary differential equations (ODEs). These deterministic models yield pre-dictable results which allow researchers to make informed recommendations on public policy. A common immigration, natural death, and fission ODE model is derived from a quantum mechanics view. This macroscopic ODE predicts that there is only one stable equilibrium point . We therefore presume that as t → ∞, the expected value should be . The quantum framework presented here yields the same standard ODE model, however with very unexpected quantum results, namely . The obvious questions are: why isn’t , why are the probabilities ≈ 0.37, and where is the missing probability of 0.26? The answer lies in quantum tunneling of probabilities. The goal of this paper is to study these tunneling effects that give specific predictions of the uncertainty in the population at the macroscopic level. These quantum effects open the poss...

Equivalence between classical epidemic model and non-dissipative and dissipative quantum tight-binding model

2020

The equivalence between classical epidemic model and non-dissipative and dissipative quantum tight-binding model is derived. Classical epidemic model can reproduce the quantum entanglement emerging in the case of electrostatically coupled qubits described by von-Neumann entropy both in non-dissipative and dissipative case. The obtained results shows that quantum mechanical phenomena might be almost entirely simulated by classical statistical model. It includes the quantum like entanglement and superposition of states. Therefore coupled epidemic models expressed by classical systems in terms of classical physics can be the base for possible incorporation of quantum technologies and in particular for quantum like computation and quantum like communication. The classical density matrix is derived and described by the equation of motion in terms of anticommutator. Existence of Rabi like oscillations is pointed in classical epidemic model. Furthermore the existence of Aharonov-Bohm effec...

A Contextual Quantum-Based Formalism for Population Dynamics

2010

Abstract Population ecology is mainly based on nonlinear equations of the Lotka-Volterra type, which provide mathematical models for describing the dynamics of interacting species. However, for many interacting populations, these equations entail complex dynamical behavior and unpredictability, generating such difficulties and problematical situations as illustrated by the “paradox of the plankton” and the “paradox of enrichment”, for instance.

A stochastic model as a survival strategy for an infected population

Scientia Plena, 2022

Complex Systems is a branch of Statistical Mechanics that has gained great notoriety in recent years. In particular, Cellular Automata are a simple way to represent complex dynamical systems in which space and time are discrete. In addition to the high degree of nonlinearity, the Boltzmann-Gibbs formalism fails due to the non-extensibility of the systems. In some cases, Complex Systems appear at the typical scale, such as stock market fluctuations for example. In the case of epidemic modeling, cellular automata are used in the description of contagion processes, such phenomena are complex and have large-scale correlations. In this sense, cellular automata present a robust and precise tool for quantifying the spread of diseases in a population provided. In our work, we reported the temporal evolution of an infection in the square network, counting process is to introduce an interaction between first neighbors and the population in which the infection acts remains constant. We obtained, through the fourth-order Binder's cumulative, the instant of time when the peak of the infection occurs, we also carried out the characterization of the type of passage through which the system goes through. We also analyzed the impact that the parameter causes on the temporal evolution of the infection.

Mathematical Modeling and Role of Dynamics in Epidemiology

2013

This study aims at providing the Considerable role of correlation of mathematical modeling and dynamical aspects of some epidemic diseases. This study emphasizes an understanding of deterministic modelling applied to the population dynamics of infection diseases. Here we are mainly emphasizing the historical background of mathematical modelling and role of dynamics in different infection diseases such as measles, AIDS, Cholera, Plague, Malaria, T.B., and Dengue etc. Our investigation is focusing on historical aspects of bioepidemiological mathematical survey. Keyword: Mathematical modelling, Epidemic disease, Biomathematical aspects, Dynamics.

A note on the roles of quantum and mechanical models in social biophysics

Recent advances in the applications of quantum models into various disciplines such as cognitive science, social sciences, economics, and biology witnessed enormous achievements and possible future progress. In this paper, we propose one of the most promising directions in the applications of quantum models: the combination of quantum and mechanical models in social biophysics. The possible resulting discipline may be called as experimental quantum social biophysics and could foster our understandings of the relationships between the society and individuals.