arXiv subjects

L. D. Valdez

Publications and source records attributed to L. D. Valdez.

At least 19 recordsLinked to original sources

arXiv2026

Household Bubbling Strategies for Epidemic Control and Social Connectivity

During the COVID-19 crisis, policymakers have implemented social bubble merging strategies, which allowed people from different households to meet and interact. Although these measures can mitigate the negative effects of extreme isolation, they also introduce additional contacts that may facilitate disease spread. As a result, several modeling studies have explored the epidemiological impact of different household-merging strategies, in which the selection of households to be merged is guided by specific demographic criteria, such as household size or the age composition of their members. Here, we investigate an alternative pairing strategy in which households are merged according to the number of economically active (working) members. We develop a mathematical model of household networks using real demographic data from multiple regions around the world, and simulate a lockdown scenario in which only economically active individuals can leave their households, while the remaining non-working members stay indoors. By using numerical simulations and the generating function technique, we then estimate the epidemic risk for different household merging strategies. We find that merging strategies based on the number of working members can keep epidemic risk at similar levels as those based on household size. Moreover, the worker-based approach allows significantly more people to form larger social bubbles, exceeding 40\% of the population in some countries. We find that merging households with at most one worker provides the best balance between controlling epidemic risk and addressing people's need for social contact.

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arXiv2026

Nonmonotonic percolation threshold in correlated networks and hypergraphs

We study the effect of assortative and disassortative mixing on the robustness of networks under random node failures. For ordinary (dyadic) networks, by using the generating function technique and stochastic simulations, we show that the relationship between the Pearson assortativity coefficient $r$ and the percolation threshold $p_c$ is not always monotonic. More specifically, in certain regions of the parameter space of our model, moderately disassortative networks can be more fragile than either strongly disassortative or uncorrelated networks. We observe this nonmonotonic behavior for trimodal networks as well as for networks with Poisson and power-law degree distributions. We then extend our analysis to hypergraphs with correlations between node hyperdegree and hyperedge cardinality. For this case, we find that positively correlated hypergraphs tend to be more fragile than negatively correlated ones. Additionally, as in the dyadic case, the relationship between $r$ and $p_c$ is nonmonotonic, and the most fragile configuration does not correspond to the most assortative hypergraph.

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arXiv2025

Superexponential growth of epidemics in networks with cliques

Many dynamic processes on complex networks, from disease outbreaks to cascading failures, can rapidly accelerate once a critical threshold is exceeded, potentially leading to severe social and economic costs. Therefore, in order to develop effective mitigation strategies, it is essential to understand how these catastrophic events occur. In this work, we investigate the dynamic of disease propagation on networks with fully connected sub-graphs (or cliques) using a susceptible-infected-quarantined (SIQ) model, and considering a scenario where only a proportion $f$ of the population has access to testing. For this model, we derive the time-evolution equations governing the spread of epidemics and show that the final proportion of infected individuals undergoes a sudden transition at a critical threshold $f_c$. Moreover, close to this transition point, our results on the time evolution of the SIQ model reveal that the number of new cases can exhibit a faster-than-exponential growth. This accelerated spread dynamics is more likely to occur in networks with larger cliques.

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arXiv2023

Explosive epidemic transitions induced by quarantine fatigue

Quarantine measures are one of the first lines of defense against the spread of infectious diseases. However, maintaining these measures over extended periods can be challenging due to a phenomenon known as quarantine fatigue. In this paper, we investigate the impact of quarantine fatigue on the spread of infectious diseases by using an epidemic model on random networks with cliques. In our model, susceptible individuals can be quarantined up to $n$ times, after which they stop complying with quarantine orders due to fatigue. Our results show that quarantine fatigue may induce a regime in which increasing the probability of detecting and isolating infected individuals (along with their close contacts) could subsequently increase the expected number of cases at the end of an outbreak. Moreover, we observe that quarantine fatigue can trigger an abrupt phase transition at the critical reproduction number $R_0=1$. Finally, we explore a scenario where a non-negligible number of individuals are infected at the beginning of an epidemic, and our results show that, depending on the value of $n$, an abrupt transition between a controlled epidemic and a large epidemic event can occur for $R_0<1$.

q-bio.PE↗

arXiv2023

Epidemic control in networks with cliques

Social units, such as households and schools, can play an important role in controlling epidemic outbreaks. In this work, we study an epidemic model with a prompt quarantine measure on networks with cliques (a $clique$ is a fully connected subgraph representing a social unit). According to this strategy, newly infected individuals are detected and quarantined (along with their close contacts) with probability $f$. Numerical simulations reveal that epidemic outbreaks in networks with cliques are abruptly suppressed at a transition point $f_c$. However, small outbreaks show features of a second-order phase transition around $f_c$. Therefore, our model can exhibit properties of both discontinuous and continuous phase transitions. Next, we show analytically that the probability of small outbreaks goes continuously to 1 at $f_c$ in the thermodynamic limit. Finally, we find that our model exhibits a backward bifurcation phenomenon.

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arXiv2022

Emergent networks in fractional percolation

Real networks are vulnerable to random failures and malicious attacks. However, when a node is harmed or damaged, it may remain partially functional, which helps to maintain the overall network structure and functionality. In this paper, we study the network structure for a fractional percolation process [Shang, Phys. Rev. E 89, 012813 (2014)], in which the state of a node can be either fully functional (FF), partially functional (PF), or dysfunctional (D). We develop new equations to calculate the relative size of the percolating cluster of FF and PF nodes, that are in agreement with our stochastic simulations. In addition, we find a regime in which the percolating cluster can be described as a coarse-grained bipartite network, namely, as a set of finite groups of FF nodes connected by PF nodes. Moreover, these groups behave as a set of "supernodes" with a power-law degree distribution. Finally, we show how this emergent structure explains the values of several critical exponents around the percolation threshold.

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arXiv2020

Epidemic spreading on modular networks: The fear to declare a pandemic

In the past few decades, the frequency of pandemics has been increased due to the growth of urbanization and mobility among countries. Since a disease spreading in one country could become a pandemic with a potential worldwide humanitarian and economic impact, it is important to develop models to estimate the probability of a worldwide pandemic. In this paper, we propose a model of disease spreading in a structural modular complex network (having communities) and study how the number of bridge nodes $n$ that connect communities affects disease spread. We find that our model can be described at a global scale as an infectious transmission process between communities with global infectious and recovery time distributions that depend on the internal structure of each community and $n$. We find that near the critical point as $n$ increases, the disease reaches most of the communities, but each community has only a small fraction of recovered nodes. In addition, we obtain that in the limit $n \to \infty$, the probability of a pandemic increases abruptly at the critical point. This scenario could make the decision on whether to launch a pandemic alert or not more difficult. Finally, we show that link percolation theory can be used at a global scale to estimate the probability of a pandemic since the global transmissibility between communities has a weak dependence on the global recovery time.

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arXiv2019

Insights into bootstrap percolation: Its equivalence with k-core percolation and the giant component

K-core and bootstrap percolation are widely studied models that have been used to represent and understand diverse deactivation and activation processes in natural and social systems. Since these models are considerably similar, it has been suggested in recent years that they could be complementary. In this manuscript we provide a rigorous analysis that shows that for any degree and threshold distributions heterogeneous bootstrap percolation can be mapped into heterogeneous k-core percolation and vice versa, if the functionality thresholds in both processes satisfy a complementary relation. Another interesting problem in bootstrap and k-core percolation is the fraction of nodes belonging to their giant connected components $P_{\infty b}$ and $P_{\infty c}$, respectively. We solve this problem analytically for arbitrary randomly connected graphs and arbitrary threshold distributions, and we show that $P_{\infty b}$ and $P_{\infty c}$ are not complementary. Our theoretical results coincide with computer simulations in the limit of very large graphs. In bootstrap percolation, we show that when using the branching theory to compute the size of the giant component, we must consider two different types of links, which are related to distinct spanning branches of active nodes.

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arXiv2017

Cascading Failures in Interdependent Networks with Multiple Supply-Demand Links and Functionality Thresholds

Various social, financial, biological and technological systems can be modeled by interdependent networks. It has been assumed that in order to remain functional, nodes in one network must receive the support from nodes belonging to different networks. So far these models have been limited to the case in which the failure propagates across networks only if the nodes lose all their supply nodes. In this paper we develop a more realistic model for two interdependent networks in which each node has its own supply threshold, i.e., they need the support of a minimum number of supply nodes to remain functional. In addition, we analyze different conditions of internal node failure due to disconnection from nodes within its own network. We show that several local internal failure conditions lead to similar nontrivial results. When there are no internal failures the model is equivalent to a bipartite system, which can be useful to model a financial market. We explore the rich behaviors of these models that include discontinuous and continuous phase transitions. Using the generating functions formalism, we analytically solve all the models in the limit of infinitely large networks and find an excellent agreement with the stochastic simulations.

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arXiv2017

Impact of rainfall on Aedes aegypti populations

Aedes aegypti is the main vector of multiple diseases, such as Dengue, Zika, and Chikungunya. Due to modifications in weather patterns, its geographical range is continuously evolving. Temperature is a key factor for its expansion into regions with cool winters, but rainfall can also have a strong impact on the colonization of these regions, since larvae emerging after a rainfall are likely to die at temperatures below $10^{\circ}$C. As climate change is expected to affect rainfall regimes, with a higher frequency of heavy storms and an increase in drought-affected areas, it is important to understand how different rainfall scenarios may shape Ae. aegypti's range. We develop a model for the population dynamics of Ae. aegypti, coupled with a rainfall model to study the effect of the temporal distribution of rainfall on mosquito abundance. Using a fracturing process, we then investigate the effect of a higher variability in the daily rainfall. As an example, we show that rainfall distribution is necessary to explain the geographic range of Ae. aegypti in Taiwan, an island characterized by rainy winters in the north and dry winters in the south. We also predict that a higher variability in the rainfall time distribution will decrease the maximum abundance of Ae. aegypti during the summer. An increase in daily rainfall variability will likewise enhance its extinction probability. Finally, we obtain a nonlinear relationship between dry season duration and extinction probability. These findings can have a significant impact on our ability to predict disease outbreaks.

q-bio.PE↗

arXiv2017

Effects of rainfall on Culex mosquito population dynamics

The dynamics of a mosquito population depends heavily on climatic variables such as temperature and precipitation. Since climate change models predict that global warming will impact on the frequency and intensity of rainfall, it is important to understand how these variables affect the mosquito populations. We present a model of the dynamics of a {\it Culex quinquefasciatus} mosquito population that incorporates the effect of rainfall and use it to study the influence of the number of rainy days and the mean monthly precipitation on the maximum yearly abundance of mosquitoes $M_{max}$. Additionally, using a fracturing process, we investigate the influence of the variability in daily rainfall on $M_{max}$. We find that, given a constant value of monthly precipitation, there is an optimum number of rainy days for which $M_{max}$ is a maximum. On the other hand, we show that increasing daily rainfall variability reduces the dependence of $M_{max}$ on the number of rainy days, leading also to a higher abundance of mosquitoes for the case of low mean monthly precipitation. Finally, we explore the effect of the rainfall in the months preceding the wettest season, and we obtain that a regimen with high precipitations throughout the year and a higher variability tends to advance slightly the time at which the peak mosquito abundance occurs, but could significantly change the total mosquito abundance in a year.

q-bio.PE↗

arXiv2016

Failure-recovery model with competition between failures in complex networks: a dynamical approach

Real systems are usually composed by units or nodes whose activity can be interrupted and restored intermittently due to complex interactions not only with the environment, but also with the same system. Majdandžić $et\;al.$ [Nature Physics 10, 34 (2014)] proposed a model to study systems in which active nodes fail and recover spontaneously in a complex network and found that in the steady state the density of active nodes can exhibit an abrupt transition and hysteresis depending on the values of the parameters. Here we investigate a model of recovery-failure from a dynamical point of view. Using an effective degree approach we find that the systems can exhibit a temporal sharp decrease in the fraction of active nodes. Moreover we show that, depending on the values of the parameters, the fraction of active nodes has an oscillatory regime which we explain as a competition between different failure processes. We also find that in the non-oscillatory regime, the critical fraction of active nodes presents a discontinuous drop which can be related to a "targeted" k-core percolation process. Finally, using mean field equations we analyze the space of parameters at which hysteresis and oscillatory regimes can be found.

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arXiv2015

Predicting the extinction of Ebola spreading in Liberia due to mitigation strategies

The Ebola virus is spreading throughout West Africa and is causing thousands of deaths. In order to quantify the effectiveness of different strategies for controlling the spread, we develop a mathematical model in which the propagation of the Ebola virus through Liberia is caused by travel between counties. For the initial months in which the Ebola virus spreads, we find that the arrival times of the disease into the counties predicted by our model are compatible with World Health Organization data, but we also find that reducing mobility is insufficient to contain the epidemic because it delays the arrival of Ebola virus in each county by only a few weeks. We study the effect of a strategy in which safe burials are increased and effective hospitalisation instituted under two scenarios: (i) one implemented in mid-July 2014 and (ii) one in mid-August---which was the actual time that strong interventions began in Liberia. We find that if scenario (i) had been pursued the lifetime of the epidemic would have been three months shorter and the total number of infected individuals 80\% less than in scenario (ii). Our projection under scenario (ii) is that the spreading will stop by mid-spring 2015.

q-bio.PE↗

arXiv2014

Triple point induced by targeted autonomization on interdependent scale free networks

Many man-made networks support each other to provide efficient services and resources to the customers, despite that this support produces a strong interdependency between the individual networks. Thus an initial failure of a fraction $1-p$ of nodes in one network, exposes the system to cascade of failures and, as a consequence, to a full collapse of the overall system. Therefore it is important to develop efficient strategies to avoid the collapse by increasing the robustness of the individual networks against failures. Here, we provide an exact theoretical approach to study the evolution of the cascade of failures on interdependent networks when a fraction $α$ of the nodes with higher connectivity in each individual network are autonomous. With this pattern of interdependency we found, for pair of heterogeneous networks, two critical percolation thresholds that depend on $α$, separating three regimes with very different network's final sizes that converge into a triple point in the plane $p-α$. Our findings suggest that the heterogeneity of the networks represented by high degree nodes is the responsible of the rich phase diagrams found in this and other investigations.

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arXiv2013

Triple Point in Correlated Interdependent Networks

Many real-world networks depend on other networks, often in non-trivial ways, to maintain their functionality. These interdependent "networks of networks" are often extremely fragile. When a fraction $1-p$ of nodes in one network randomly fails, the damage propagates to nodes in networks that are interdependent and a dynamic failure cascade occurs that affects the entire system. We present dynamic equations for two interdependent networks that allow us to reproduce the failure cascade for an arbitrary pattern of interdependency. We study the "rich club" effect found in many real interdependent network systems in which the high-degree nodes are extremely interdependent, correlating a fraction $α$ of the higher degree nodes on each network. We find a rich phase diagram in the plane $p-α$, with a triple point reminiscent of the triple point of liquids that separates a non-functional phase from two functional phases.

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arXiv2013

Social distancing strategies against disease spreading

The recurrent infectious diseases and their increasing impact on the society has promoted the study of strategies to slow down the epidemic spreading. In this review we outline the applications of percolation theory to describe strategies against epidemic spreading on complex networks. We give a general outlook of the relation between link percolation and the susceptible-infected-recovered model, and introduce the node void percolation process to describe the dilution of the network composed by healthy individual, $i.e$, the network that sustain the functionality of a society. Then, we survey two strategies: the quenched disorder strategy where an heterogeneous distribution of contact intensities is induced in society, and the intermittent social distancing strategy where health individuals are persuaded to avoid contact with their neighbors for intermittent periods of time. Using percolation tools, we show that both strategies may halt the epidemic spreading. Finally, we discuss the role of the transmissibility, $i.e$, the effective probability to transmit a disease, on the performance of the strategies to slow down the epidemic spreading.

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arXiv2013

Temporal percolation of a susceptible adaptive network

In the last decades, many authors have used the susceptible-infected-recovered model to study the impact of the disease spreading on the evolution of the infected individuals. However, few authors focused on the temporal unfolding of the susceptible individuals. In this paper, we study the dynamic of the susceptible-infected-recovered model in an adaptive network that mimics the transitory deactivation of permanent social contacts, such as friendship and work-ship ties. Using an edge-based compartmental model and percolation theory, we obtain the evolution equations for the fraction susceptible individuals in the susceptible biggest component. In particular, we focus on how the individual's behavior impacts on the dilution of the susceptible network. We show that, as a consequence, the spreading of the disease slows down, protecting the biggest susceptible cluster by increasing the critical time at which the giant susceptible component is destroyed. Our theoretical results are fully supported by extensive simulations.

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arXiv2012

Temporal percolation of the susceptible network in an epidemic spreading

In this work, we study the evolution of the susceptible individuals during the spread of an epidemic modeled by the susceptible-infected-recovered (SIR) process spreading on the top of complex networks. Using an edge-based compartmental approach and percolation tools, we find that a time-dependent quantity $Φ_S(t)$, namely, the probability that a given neighbor of a node is susceptible at time $t$, is the control parameter of a node void percolation process involving those nodes on the network not-reached by the disease. We show that there exists a critical time $t_c$ above which the giant susceptible component is destroyed. As a consequence, in order to preserve a macroscopic connected fraction of the network composed by healthy individuals which guarantee its functionality, any mitigation strategy should be implemented before this critical time $t_c$. Our theoretical results are confirmed by extensive simulations of the SIR process.

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