Optimal allocation of resources for suppressing epidemic spreading on networks

Deciphering population-level response under spatial drug heterogeneity on microhabitat structures

Bacteria and cancer cells live in a spatially heterogeneous environment, where migration shapes the microhabitat structures critical for colonization and metastasis. The interplay between growth, migration, and microhabitat structure complicates the prediction of population responses to drugs, such as clearance or sustained growth, posing a longstanding challenge. Here, we disentangle growth-migration dynamics and identify that population decline is determined by two decoupled terms: a spatial growth variation term and a microhabitat structure term. Notably, the microhabitat structure term can be interpreted as a dynamic-related centrality measure. For fixed spatial drug arrangements, we show that interpreting these centralities reveals how different network structures, even with identical edge densities, microhabitat numbers, and spatial heterogeneity, can lead to distinct population-level responses. Increasing edge density shifts the population response from growth to clearance, supporting an inversed centrality-connectivity relationship, and mirroring the effects of higher migration rates. Furthermore, we derive a sufficient condition for robust population decline across various spatial growth rate arrangements, regardless of spatial-temporal fluctuations induced by drugs. Additionally, we demonstrate that varying the maximum growth-to-death ratio, determined by drug-bacteria interactions, can lead to distinct population decline profiles and a minimal decline phase emerges. These findings address key challenges in predicting population-level responses and provide insights into divergent clinical outcomes under identical drug dosages. This work may offer a new method of interpreting treatment dynamics and potential approaches for optimizing spatially explicit drug dosing strategies.

Effects of the information-driven awareness on epidemic spreading on multiplex networks

In this study, we examine the impact of information-driven awareness on the spread of an epidemic from the perspective of resource allocation by comprehensively considering a series of realistic scenarios. A coupled awareness-resource-epidemic model on top of multiplex networks is proposed, and a Microscopic Markov Chain Approach is adopted to study the complex interplay among the processes. Through theoretical analysis, the infection density of the epidemic is predicted precisely, and an approximate epidemic threshold is derived. Combining both numerical calculations and extensive Monte Carlo simulations, the following conclusions are obtained. First, during a pandemic, the more active the resource support between individuals, the more effectively the disease can be controlled; that is, there is a smaller infection density and a larger epidemic threshold. Second, the disease can be better suppressed when individuals with small degrees are preferentially protected. In addition, there is a critical parameter of contact preference at which the effectiveness of disease control is the worst. Third, the inter-layer degree correlation has a "double-edged sword" effect on spreading dynamics. In other words, when there is a relatively lower infection rate, the epidemic threshold can be raised by increasing the positive correlation. By contrast, the infection density can be reduced by increasing the negative correlation. Finally, the infection density decreases when raising the relative weight of the global information, which indicates that global information about the epidemic state is more efficient for disease control than local information.

Intervention of resource allocation strategies on spatial spread of epidemics

Medical resources are crucial in mitigating epidemics, especially during pandemics such as the ongoing COVID-19. Thereby, reasonable resource deployment inevitably plays a significant role in suppressing the epidemic under limited resources. When an epidemic breaks out, people can produce resources for self-protection or donate resources to help others for treatment. That is, the exchange of resources also affects the transmission between individuals, thus, altering the epidemic dynamics. To understand factors on resource deployment and the interplay between resource and transmission we construct a metapopulation network model with resource allocation. Our results indicate actively or promptly donating resources is not helpful to suppress the epidemic under both homogeneous population distribution and heterogeneous population distribution. Besides, strengthening the speed of resources production can significantly increase the recovery rate so that they reduce the final outbreak size. These results may provide policy guidance toward epidemic containment.

Modeling and controlling the spread of epidemic with various social and economic scenarios

We propose a dynamical model for describing the spread of epidemics. This model is an extension of the SIQR (susceptible-infected-quarantined-recovered) and SIRP (susceptible-infected-recovered-pathogen) models used earlier to describe various scenarios of epidemic spreading. As compared to the basic SIR model, our model takes into account two possible routes of contagion transmission: direct from the infected compartment to the susceptible compartment and indirect via some intermediate medium or fomites. Transmission rates are estimated in terms of average distances between the individuals in selected social environments and characteristic time spans for which the individuals stay in each of these environments. We also introduce a collective economic resource associated with the average amount of money or income per individual to describe the socioeconomic interplay between the spreading process and the resource available to infected individuals. The epidemic-resource coupling is supposed to be of activation type, with the recovery rate governed by the Arrhenius-like law. Our model brings an advantage of building various control strategies to mitigate the effect of epidemic and can be applied, in particular, to modeling the spread of COVID-19.

A toy model for the epidemic-driven collapse in a system with limited economic resource

ABSTRACT

Based on a toy model for a trivial socioeconomic system, we demonstrate that the activation-type mechanism of the epidemic-resource coupling can lead to the collapsing effect opposite to thermal explosion. We exploit a SIS-like (susceptible-infected-susceptible) model coupled with the dynamics of average economic resource for a group of active economic agents. The recovery rate of infected individuals is supposed to obey the Arrhenius-like law, resulting in a mutual negative feedback between the number of active agents and resource acquisition. The economic resource is associated with the average amount of money or income per agent and formally corresponds to the effective market temperature of agents, with their income distribution obeying the Boltzmann-Gibbs statistics. A characteristic level of resource consumption is associated with activation energy. We show that the phase portrait of the system features a collapse phase, in addition to the well-known disease-free and endemic phases. The epidemic intensified by the increasing resource deficit can ultimately drive the system to a collapse at nonzero activation energy because of limited resource. We briefly discuss several collapse mitigation strategies involving either financial instruments like subsidies or social regulations like quarantine.

GRAPHIC ABSTRACT

Effects of heterogeneous self-protection awareness on resource-epidemic coevolution dynamics

Recent studies have demonstrated that the allocation of individual resources has a significant influence on the dynamics of epidemic spreading. In the real scenario, individuals have a different level of awareness for self-protection when facing the outbreak of an epidemic. To investigate the effects of the heterogeneous self-awareness distribution on the epidemic dynamics, we propose a resource-epidemic coevolution model in this paper. We first study the effects of the heterogeneous distributions of node degree and self-awareness on the epidemic dynamics on artificial networks. Through extensive simulations, we find that the heterogeneity of self-awareness distribution suppresses the outbreak of an epidemic, and the heterogeneity of degree distribution enhances the epidemic spreading. Next, we study how the correlation between node degree and self-awareness affects the epidemic dynamics. The results reveal that when the correlation is positive, the heterogeneity of self-awareness restrains the epidemic spreading. While, when there is a significant negative correlation, strong heterogeneous or strong homogeneous distribution of the self-awareness is not conducive for disease suppression. We find an optimal heterogeneity of self-awareness, at which the disease can be suppressed to the most extent. Further research shows that the epidemic threshold increases monotonously when the correlation changes from most negative to most positive, and a critical value of the correlation coefficient is found. When the coefficient is below the critical value, an optimal heterogeneity of self-awareness exists; otherwise, the epidemic threshold decreases monotonously with the decline of the self-awareness heterogeneity. At last, we verify the results on four typical real-world networks and find that the results on the real-world networks are consistent with those on the artificial network.

Coevolution spreading in complex networks

The propagations of diseases, behaviors and information in real systems are rarely independent of each other, but they are coevolving with strong interactions. To uncover the dynamical mechanisms, the evolving spatiotemporal patterns and critical phenomena of networked coevolution spreading are extremely important, which provide theoretical foundations for us to control epidemic spreading, predict collective behaviors in social systems, and so on. The coevolution spreading dynamics in complex networks has thus attracted much attention in many disciplines. In this review, we introduce recent progress in the study of coevolution spreading dynamics, emphasizing the contributions from the perspectives of statistical mechanics and network science. The theoretical methods, critical phenomena, phase transitions, interacting mechanisms, and effects of network topology for four representative types of coevolution spreading mechanisms, including the coevolution of biological contagions, social contagions, epidemic-awareness, and epidemic-resources, are presented in detail, and the challenges in this field as well as open issues for future studies are also discussed.

Cooperative epidemics spreading under resource control

The input and allocation of public resources are of crucial importance to suppressing the outbreak of infectious diseases. However, in the research on multi-disease dynamics, the impact of resources has never been taken into account. Here, we propose a two-epidemic spreading model with resource control, in which the amount of resources is introduced into the recovery rates of diseases and the allocation of resources between two diseases is regulated by a parameter. Using the dynamical message passing method, we obtain resource thresholds of the two diseases and validate them on ER networks and scale-free networks. By comparing the results on scale-free networks with different power-law exponents, we find that the heterogeneity of the network promotes the spreading of both diseases. Especially, we find optimal allocation coefficients at different resource levels. And, we get a counterintuitive conclusion that when the available resources are limited, it is a better strategy to preferentially suppress the disease with lower infection rate. In addition, we investigate the effect of interaction strength and find that great interaction strength between diseases makes two diseases with different infectivity tend to be homogeneous.

Resource control of epidemic spreading through a multilayer network

While the amount of resource is an important factor in control of contagions, outbreaks may occur when they reach a finite fraction of the population. An unexplored issue is how much the resource amount is invested to control this outbreak. Here we analyze a mechanic model of epidemic spreading, which considers both resource factor and network layer. We find that there is a resource threshold, such that a significant fraction of the total population may be infected (i.e., an outbreak will occur) if the amount of resource is below this threshold, but the outbreak may be effectively eradicated if it is beyond the threshold. The threshold is dependent upon both the connection strength between the layers and their internal structure. We also find that the layer-layer connection strength can lead to the phase transition from the first-order phase to the continuous one or vice versa, whereas the internal connection can result in a different kind of phase transition (i.e., the so-called hybrid phase transition) apart from first-order and continuous one. Our results could have important implications for government decisions on public health resources devoted to epidemic disease control.