Modelling contagious viral dynamics: a kinetic approach based on mutual utility
arXiv:2401.00480 · doi:10.3934/mbe.2024187
Abstract
The temporal evolution of a contagious viral disease is modelled as the dynamic progression of different classes of population with individuals interacting pairwise. This interaction follows a binary mechanism typical of kinetic theory, wherein agents aim to improve their condition with respect to a mutual utility target. To this end, we introduce kinetic equations of Boltzmann-type to describe the time evolution of the probability distributions of the multi-agent system. The interactions between agents are defined using principles from price theory, specifically employing Cobb-Douglas utility functions for binary exchange and the Edgeworth box to depict the common exchange area where utility increases for both agents. Several numerical experiments presented in the paper highlight the significance of this mechanism in driving the phenomenon toward endemicity.
References in corpus (13)
- Wealth distribution under the spread of infectious diseases
- Kinetic models for the trading of goods
- Hyperbolic models for the spread of epidemics on networks: kinetic description and numerical methods
- Self-similarity and power-like tails in nonconservative kinetic models
- Optimal control of epidemic spreading in presence of social heterogeneity
- Spatial spread of COVID-19 outbreak in Italy using multiscale kinetic transport equations with uncertainty
- Kinetic modelling of epidemic dynamics: social contacts, control with uncertain data, and multiscale spatial dynamics
- Asymptotic-Preserving Neural Networks for multiscale hyperbolic models of epidemic spread
- An SIR model with viral load-dependent transmission
- An SIR-like kinetic model tracking individuals' viral load
- Bi-fidelity stochastic collocation methods for epidemic transport models with uncertainties
- From agent-based models to the macroscopic description of fake-news spread: the role of competence in data-driven applications
- Asymptotic-Preserving Neural Networks for hyperbolic systems with diffusive scaling