arXiv subjects

Simon Levin

Publications and source records attributed to Simon Levin.

7 recordsLinked to original sources

arXiv2025

Spatial modeling of forest-savanna bistability: Impacts of fire dynamics and timescale separation

Forest-savanna bistability - the hypothesis that forests and savannas exist as alternative stable states in the tropics - and its implications are key challenges for mathematical modelers and ecologists in the context of ongoing climate change. To generate new insights into this problem, we present a spatial Markov jump process model of savanna forest fires that integrates key ecological processes, including seed dispersal, fire spread, and non-linear vegetation flammability. In contrast to many models of forest-savanna bistability, we explicitly model both fire dynamics and vegetation regrowth in a mathematically tractable framework. This approach bridges the gap between slow-timescale vegetation models and highly resolved fire dynamics, shedding light on the influence of short-term and transient processes on vegetation cover. In our spatial stochastic model, bistability arises from periodic fires that maintain low forest cover, whereas dense forest areas inhibit fire spread and preserve high tree density. The deterministic mean-field approximation of the model similarly predicts bistability, but deviates quantitatively from the fully spatial model, especially in terms of its transient dynamics. These results also underscore the critical role of timescale separation between fire and vegetation processes in shaping ecosystem structure and resilience.

q-bio.PE↗

arXiv2024

The Complex Interplay Between Risk Tolerance and the Spread of Infectious Diseases

Risk-driven behavior provides a feedback mechanism through which individuals both shape and are collectively affected by an epidemic. We introduce a general and flexible compartmental model to study the effect of heterogeneity in the population with regards to risk tolerance. The interplay between behavior and epidemiology leads to a rich set of possible epidemic dynamics. Depending on the behavioral composition of the population, we find that increasing heterogeneity in risk tolerance can either increase or decrease the epidemic size. We find that multiple waves of infection can arise due to the interplay between transmission and behavior, even without the replenishment of susceptibles. We find that increasing protective mechanisms such as the effectiveness of interventions, the number of risk-averse people in the population, and the duration of intervention usage reduces the epidemic overshoot. When the protection is pushed past a critical threshold, the epidemic dynamics enter an underdamped regime where the epidemic size exactly equals the herd immunity threshold. Lastly, we can find regimes where epidemic size does not monotonically decrease with a population that becomes increasingly risk-averse.

physics.soc-ph↗

arXiv2023

Commutativity and Null Spaces of Unbounded Operators on Hilbert Space

Based on the success of a well-known method for solving higher order linear differential equations, a study of two of the most important mathematical features of that method, viz. the null spaces and commutativity of the product of unbounded linear operators on a Hilbert space is carried out. A principle is proved describing solutions for the product of such operators in terms of the solutions for each of the factors when the null spaces of those factors satisfy a certain geometric relation to one another. Another geometric principle equating commutativity of a closed densely defined operator and a projection to stability of the range of the projection under the closed operator is proved.

math.FA↗

arXiv2023

Active risk aversion in SIS epidemics on networks

We present and analyze an actively controlled Susceptible-Infected-Susceptible (actSIS) model of interconnected populations to study how risk aversion strategies, such as social distancing, affect network epidemics. A population using a risk aversion strategy reduces its contact rate with other populations when it perceives an increase in infection risk. The network actSIS model relies on two distinct networks. One is a physical contact network that defines which populations come into contact with which other populations and thus how infection spreads. The other is a communication network, such as an online social network, that defines which populations observe the infection level of which other populations and thus how information spreads. We prove that the model, with these two networks and populations using risk aversion strategies, exhibits a transcritical bifurcation in which an endemic equilibrium emerges. For regular graphs, we prove that the endemic infection level is uniform across populations and reduced by the risk aversion strategy, relative to the network SIS endemic level. We show that when communication is sufficiently sparse, this initially stable equilibrium loses stability in a secondary bifurcation. Simulations show that a new stable solution emerges with nonuniform infection levels.

q-bio.PE↗

arXiv2023

Fundamental Bound on Epidemic Overshoot in the SIR Model

We derive an exact upper bound on the epidemic overshoot for the Kermack-McKendrick SIR model. This maximal overshoot value of 0.2984... occurs at $R_0^*$ = 2.151... . In considering the utility of the notion of overshoot, a rudimentary analysis of data from the first wave of the COVID-19 pandemic in Manaus, Brazil highlights the public health hazard posed by overshoot for epidemics with $R_0$ near 2. Using the general analysis framework presented within, we then consider more complex SIR models that incorporate vaccination.

q-bio.PE↗

arXiv2022

Socio-Political Feedback on the Path to Net Zero

Anthropogenic emissions of CO2 must soon approach net-zero to stabilize the global mean temperature. Although several international agreements have advocated for coordinated climate actions, their implementation has remained below expectations. One of the main challenges of international cooperation is the different degrees of socio-political acceptance of decarbonization. Here we interrogate a minimalistic model of the coupled natural-human system representing the impact of such socio-political acceptance on clean energy investments and the path to net-zero emissions. We show that incentives and carbon pricing are essential tools to achieve net-zero before critical CO2 concentrations are reached, and deep international coordination is necessary for a rapid and effective transition. Although a perfect coordination scenario remains unlikely, as investments in clean energy are ultimately limited by myopic economic strategies and a policy system that promotes free-riding, more realistic decentralized cooperation with partial efforts from each actor could still lead to significant emissions cuts.

physics.soc-ph↗

arXiv2003

Equation-free modeling of evolving diseases: Coarse-grained computations with individual-based models

We demonstrate how direct simulation of stochastic, individual-based models can be combined with continuum numerical analysis techniques to study the dynamics of evolving diseases. % Sidestepping the necessity of obtaining explicit population-level models, the approach analyzes the (unavailable in closed form) `coarse' macroscopic equations, estimating the necessary quantities through appropriately initialized, short `bursts' of individual-based dynamic simulation. % We illustrate this approach by analyzing a stochastic and discrete model for the evolution of disease agents caused by point mutations within individual hosts. % Building up from classical SIR and SIRS models, our example uses a one-dimensional lattice for variant space, and assumes a finite number of individuals. % Macroscopic computational tasks enabled through this approach include stationary state computation, coarse projective integration, parametric continuation and stability analysis.

nlin.AO↗