An official website of the United States government
Abstract We analytically study the emergence of instabilities and the consequent steady-state pattern formation in a stochastic partial differential equation (PDE) based, compartmental model of spatiotemporal epidemic spread. The model is characterized by: (1) strongly nonlinear forces representing the infection transmission mechanism and (2) random environmental forces represented by the Ornstein–Uhlenbeck (O–U) stochastic process which better approximates real-world uncertainties. Employing second-order perturbation analysis and computing the local Lyapunov exponent, we find the emergence of diffusion-induced instabilities and analyze the effects of O–U noise on these instabilities. We obtain a range of values of the diffusion coefficient and correlation time in parameter space that support the onset of instabilities. Notably, the stability and pattern formation results depend critically on the correlation time of the O–U stochastic process; specifically, we obtain lower values of steady-state infection density for higher correlation times. Also, for lower correlation times the results approach those obtained in the white noise case. The analytical results are valid for lower-order correlation times. In summary, the results provide insights into the onset of noise-induced, and Turing-type instabilities in a stochastic PDE epidemic model in the presence of strongly nonlinear deterministic infection forces and stochastic environmental forces represented by Ornstein–Uhlenbeck noise.
more »
« less
Instabilities and self–organization in spatiotemporal epidemic dynamics driven by nonlinearity and noise
Abstract Theoretical analysis of epidemic dynamics has attracted significant attention in the aftermath of the COVID–19 pandemic. In this article, we study dynamic instabilities in a spatiotemporal compartmental epidemic model represented by a stochastic system of coupled partial differential equations (SPDE). Saturation effects in infection spread–anchored in physical considerations–lead to strong nonlinearities in the SPDE. Our goal is to study the onset of dynamic, Turing–type instabilities, and the concomitant emergence of steady–state patterns under the interplay between three critical model parameters–the saturation parameter, the noise intensity, and the transmission rate. Employing a second–order perturbation analysis to investigate stability, we uncover both diffusion–driven and noise–induced instabilities and corresponding self–organized distinct patterns of infection spread in the steady state. We also analyze the effects of the saturation parameter and the transmission rate on the instabilities and the pattern formation. In summary, our results indicate that the nuanced interplay between the three parameters considered has a profound effect on the emergence of dynamical instabilities and therefore on pattern formation in the steady state. Moreover, due to the central role played by the Turing phenomenon in pattern formation in a variety of biological dynamic systems, the results are expected to have broader significance beyond epidemic dynamics.
more »
« less
- PAR ID:
- 10522547
- Publisher / Repository:
- IOP Publishing
- Date Published:
- Journal Name:
- Physical Biology
- Volume:
- 21
- Issue:
- 4
- ISSN:
- 1478-3967
- Format(s):
- Medium: X Size: Article No. 046001
- Size(s):
- Article No. 046001
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
It is well recognized that population heterogeneity plays an important role in the spread of epidemics. While individual variations in social activity are often assumed to be persistent, that is, constant in time, here we discuss the consequences of dynamic heterogeneity. By integrating the stochastic dynamics of social activity into traditional epidemiological models, we demonstrate the emergence of a new long timescale governing the epidemic, in broad agreement with empirical data. Our stochastic social activity model captures multiple features of real-life epidemics such as COVID-19, including prolonged plateaus and multiple waves, which are transiently suppressed due to the dynamic nature of social activity. The existence of a long timescale due to the interplay between epidemic and social dynamics provides a unifying picture of how a fast-paced epidemic typically will transition to an endemic state.more » « less
-
McCaw, James M (Ed.)Defective interfering particles (DIPs) are virus-like particles that occur naturally during virus infections. These particles are defective, lacking essential genetic materials for replication, but they can interact with the wild-type virus and potentially be used as therapeutic agents. However, the effect of DIPs on infection spread is still unclear due to complicated stochastic effects and nonlinear spatial dynamics. In this work, we develop a model with a new hybrid method to study the spatial-temporal dynamics of viruses and DIPs co-infections within hosts. We present two different scenarios of virus production and compare the results from deterministic and stochastic models to demonstrate how the stochastic effect is involved in the spatial dynamics of virus transmission. We compare the spread features of the virus in simulations and experiments, including the formation and the speed of virus spread and the emergence of stochastic patchy patterns of virus distribution. Our simulations simultaneously capture observed spatial spread features in the experimental data, including the spread rate of the virus and its patchiness. The results demonstrate that DIPs can slow down the growth of virus particles and make the spread of the virus more patchy.more » « less
-
We analyze the driven-dissipative dynamics of subwavelength periodic atomic arrays in free space, where atoms interact via light-induced dipole-dipole interactions. We find that depending on the system parameters, the underlying mean-field model allows four different types of dynamics at late times: a single monostable steady state solution, bistability (where two stable steady state solutions exist), limit cycles and chaotic dynamics. We provide conditions on the parameters required to realize the different solutions in the thermodynamic limit. In this limit, only the monostable or bistable regime can be accessed for the parameter values accessible via light-induced dipole-dipole interactions. For finite size periodic arrays, however, we find that the mean-field dynamics of the many-body system also exhibit limit cycles and chaotic behavior. Notably, the emergence of chaotic dynamics does not rely on the randomness of an external control parameter but arises solely due to the interplay of coherent drive and dissipation. Published by the American Physical Society2025more » « less
-
Nonpharmaceutical interventions (NPIs) such as mask wearing can be effective in mitigating the spread of infectious diseases. Therefore, understanding the behavioral dynamics of NPIs is critical for characterizing the dynamics of disease spread. Nevertheless, standard infection models tend to focus only on disease states, overlooking the dynamics of “beneficial contagions,” e.g., compliance with NPIs. In this work, we investigate the concurrent spread of disease and mask-wearing behavior over multiplex networks. Our proposed framework captures both the competing and complementary relationships between the dueling contagion processes. Further, the model accounts for various behavioral mechanisms that influence mask wearing, such as peer pressure and fear of infection. Our results reveal that under the coupled disease–behavior dynamics, the attack rate of a disease—as a function of transition probability—exhibits a critical transition. Specifically, as the transmission probability exceeds a critical threshold, the attack rate decreases abruptly due to sustained mask-wearing responses. We empirically explore the causes of the critical transition and demonstrate the robustness of the observed phenomena. Our results highlight that without proper enforcement of NPIs, reductions in the disease transmission probability via other interventions may not be sufficient to reduce the final epidemic size.more » « less
