To improve the accuracy of network-based SIS models we introduce and study a multilayer represent... more To improve the accuracy of network-based SIS models we introduce and study a multilayer representation of a time-dependent network. In particular, we assume that individuals have their long-term (permanent) contacts that are always present, identifying in this way the first network layer. A second network layer also exists, where the same set of nodes can be connected by occasional links, created with a given probability. While links of the first layer are permanent, a link of the second layer is only activated with some probability and under the condition that the two nodes, connected by this link, are simultaneously participating to the temporary link. We develop a model for the SIS epidemic on this time-dependent network, analyze equilibrium and stability of the corresponding mean-field equations, and shed some light on the role of the temporal layer on the spreading process.
In this paper we study the appearance of bifurcations of limit cycles in an epidemic model with t... more In this paper we study the appearance of bifurcations of limit cycles in an epidemic model with two types of aware individuals. All the transition rates are constant except for the alerting decay rate of the most aware individuals and the rate of creation of the less aware individuals, which depend on the disease prevalence in a non-linear way. For the ODE model, the numerical computation of the limit cycles and the study of their stability are made by means of the Poincaré map. Moreover, sufficient conditions for the existence of an endemic equilibrium are also obtained. These conditions involve a rather natural relationship between the transmissibility of the disease and that of awareness. Finally, stochastic simulations of the model under a very low rate of imported cases are used to confirm the scenarios of bistability (endemic equilibrium and limit cycle) observed in the solutions of the ODE model.
Systems with many components (individuals or local populations as cities, or metropolitan areas, ... more Systems with many components (individuals or local populations as cities, or metropolitan areas, or regions, …) connected by non-trivial associations or relationships can be statistically described by means of the formalism of complex networks which is based on descriptors like degree distributions, degree-degree correlations, etc. In the last years, many researchers from different fields have been using different approaches to model processes taking place on complex networks.
We present a pair-approximation model for spatial forest dynamics defined on a regular lattice. T... more We present a pair-approximation model for spatial forest dynamics defined on a regular lattice. The model assumes three possible states for a lattice site: empty (gap site), occupied by an immature tree, and occupied by a mature tree, and considers three nonlinearities in the dynamics associated to the processes of light interference, gap expansion, and recruitment. We obtain an expression of the basic reproduction number R(0) which, in contrast to the one obtained under the mean-field approach, uses information about the spatial arrangement of individuals close to extinction. Moreover, we analyze the corresponding survival-extinction transition of the forest and the spatial correlations among gaps, immature and mature trees close to this critical point. Predictions of the pair-approximation model are compared with those of a cellular automaton.
We present the derivation of the continuous-time equations governing the limit dynamics of discre... more We present the derivation of the continuous-time equations governing the limit dynamics of discrete-time reaction-diffusion processes defined on heterogeneous metapopulations. We show that, when a rigorous time limit is performed, the lack of an epidemic threshold in the spread of infections is not limited to metapopulations with a scale-free architecture, as it has been predicted from dynamical equations in which reaction and diffusion occur sequentially in time.
After a presentation of the paper cited above at a workshop on Dynamic Networks at the Isaac Newt... more After a presentation of the paper cited above at a workshop on Dynamic Networks at the Isaac Newton Institute for Mathematical Sciences, Cambridge, prof Frank Ball in discussions explained two potential errors in our analysis. After further discussions this was indeed confirmed. One mistake was an oversight, whereas the second one was more subtle. It turns out that the first mistake has impacts on the results of the paper, whereas the second one can be repaired and hence has no effect on the results. The oversight appears in Section 4.1 where the basic reproduction number R BA
The Markovian approach, which assumes exponentially distributed interinfection times, is dominant... more The Markovian approach, which assumes exponentially distributed interinfection times, is dominant in epidemic modeling. However, this assumption is unrealistic as an individual's infectiousness depends on its viral load and varies over time. In this paper, we present a Susceptible-Infected-Recovered-Vaccinated-Susceptible epidemic model incorporating non-Markovian infection processes. The model can be easily adapted to accurately capture the generation time distributions of emerging infectious diseases, which is essential for accurate epidemic prediction. We observe noticeable variations in the transient behavior under different infectiousness profiles and the same basic reproduction number R0. The theoretical analyses show that only R0 and the mean immunity period of the vaccinated individuals have an impact on the critical vaccination rate needed to achieve herd immunity. A vaccination level at the critical vaccination rate can ensure a very low incidence among the population in the case of future epidemics, regardless of the infectiousness profiles.
This paper is concerned with the robustness of the sustained oscillations predicted by an epidemi... more This paper is concerned with the robustness of the sustained oscillations predicted by an epidemic ODE model defined on contact networks. The model incorporates the spread of awareness among individuals and, moreover, a small inflow of imported cases. These cases prevent stochastic extinctions when we simulate the epidemics and, hence, they allow to check whether the average dynamics for the fraction of infected individuals are accurately predicted by the ODE model. Stochastic simulations confirm the existence of sustained oscillations for different types of random networks, with a sharp transition from a non-oscillatory asymptotic regime to a periodic one as the alerting rate of susceptible individuals increases from very small values. This abrupt transition to periodic epidemics of high amplitude is quite accurately predicted by the Hopf-bifurcation curve computed from the ODE model using the alerting rate and the infection transmission rate for aware individuals as tuning parameters.
This paper is concerned with stochastic SIR and SEIR epidemic models on random networks in which ... more This paper is concerned with stochastic SIR and SEIR epidemic models on random networks in which individuals may rewire away from infected neighbors at some rate ω (and reconnect to non-infectious individuals with probability α or else simply drop the edge if α = 0), so-called preventive rewiring. The models are denoted SIR-ω and SEIR-ω, and we focus attention on the early stages of an outbreak, where we derive expression for the basic reproduction number R 0 and the expected degree of the infectious nodes E(D I) using two different approximation approaches. The first approach approximates the early spread of an epidemic by a branching process, whereas the second one uses pair approximation. The expressions are compared with the corresponding empirical means obtained from stochastic simulations of SIR-ω and SEIRω epidemics on Poisson and scale-free networks. Without rewiring of exposed nodes, the two approaches predict the same epidemic threshold and the same E(D I) for both types of epidemics, the latter being very close to the mean degree obtained from simulated epidemics over Poisson networks. Above the epidemic threshold, pairwise models overestimate the value of R 0 computed from simulations, which turns out to be very close to the one predicted by the branching process approximation. When exposed individuals also rewire with α > 0 (perhaps unaware of being infected), the two approaches give different epidemic thresholds, with the branching process approximation being more in agreement with simulations.
Using a bioenergetic model we show that the pattern of foraging preferences greatly determines th... more Using a bioenergetic model we show that the pattern of foraging preferences greatly determines the complexity of the resulting food webs. By complexity we refer to the degree of richness of food‐web architecture, measured in terms of some topological indicators (number of persistent species and links, connectance, link density, number of trophic levels, and frequency of weak links). The poorest food‐web architecture is found for a mean‐field scenario where all foraging preferences are assumed to be the same. Richer food webs appear when foraging preferences depend on the trophic position of species. Food‐web complexity increases with the number of basal species. We also find a strong correlation between the complexity of a trophic module and the complexity of entire food webs with the same pattern of foraging preferences.
The structural properties of the subway network are crucial in effective transportation in cities... more The structural properties of the subway network are crucial in effective transportation in cities. This paper presents an information perspective of navigation in four different subway networks: New York City, Paris, Barcelona and Moscow. We addressed our study to investigate what is that makes it complicated to navigate in these kinds of networks and we carried out a comparison between them and their intrinsic constraints. Our methodological approach is based on a set of cost/efficiency indicators which are defined in the complex networks literature. We find that the overall complexity in finding stations measured by the average search information S linearly increases as a function of the network size N. The direct implication of this finding is that from these basic levels of required information, the average value H(k) can be represented as a function of the node degree k. Finally, through analyzing subway networks in space P, we reveal the existing service modularity among subway routes using a rescaled expression of S.
We present a continuum formalism for modeling growing random networks under addition and deletion... more We present a continuum formalism for modeling growing random networks under addition and deletion of nodes based on a differential mass balance equation. As examples of its applicability, we obtain new results on the degree distribution for growing networks with a uniform attachment and deletion of nodes, and complete some recent results on growing networks with preferential attachment and uniform removal.
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service... more This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Currently, several western countries have more than half of their population fully vaccinated aga... more Currently, several western countries have more than half of their population fully vaccinated against COVID-19. At the same time, some of them are experiencing a fourth or even a fifth wave of cases, most of them concentrated in sectors of the populations whose vaccination coverage is lower than the average. So, the initial scenario of vaccine prioritization has given way to a new one where achieving herd immunity is the primary concern. Using an age-structured vaccination model with waning immunity, we show that, under a limited supply of vaccines, a vaccination strategy based on minimizing the basic reproduction number allows for the deployment of a number of vaccine doses lower than the one required for maximizing the vaccination coverage. Such minimization is achieved by giving greater protection to those age groups that, for a given social contact pattern, have smaller fractions of susceptible individuals at the endemic equilibrium without vaccination, that is, to those groups that are more vulnerable to infection. The pandemic of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is still imposing incredible pressure on many countries' healthcare and economic systems. Nations in America, Europe, Asia, and Africa have faced large numbers of deaths due to COVID 19, and a continued crisis situation. The only good news in this dark situation is that vaccines are becoming available from different companies all over the world. Some countries are currently evaluating the efficacy and effectiveness of developed vaccines, while some other countries have already started their vaccination campaign. In particular, as of November 2021, more than 75% of the people in countries like Canada, United Kingdom, and France have received at least one dose of the vaccination, while no more than 35% of people in Bangladesh, Guinea, and Armenia have received one dose at least 1. These examples give an idea of the heterogeneous situation of the vaccination campaign in the world. Additionally, current studies suggest a decay of neutralizing antibody responses in convalescent patients 2 , as well as a decline in the effectiveness of mRNA COVID-19 vaccines 3. Therefore, vaccines probably provide a short-lived immunity. For instance, comparing the rate of decay of the antibody responses following infections by human coronavirus (hCoV) and by SARS-CoV-2, it has been suggested that individuals may become susceptible to reinfection within 12-18 months after a previous infection 2. Similarly, a recent comparative evolutionary analysis of coronavirus relatives of SRAS-CoV-2 reveals that, under endemic conditions, reinfection by SARS-CoV-2 would likely occur between 3 months and 5.1 years after peak antibody response, with a median of 16 months 4. While during the ongoing pandemic most countries agree to vaccinate first public health personnel and people in long term care facilities, the limited availability of vaccines and the logistic complexities are still posing big questions on when and how the vaccination campaign will be completed. Initially, some countries assessed reaching herd immunity at around 70% of the population vaccinated 5. With time, several hurdles upon this achievement are becoming evident 6. These difficulties in obtaining herd immunity may further discouraging people from attaining it 5. Countries are now developing immunization plans to face the challenge of distributing millions of vaccines, some of which require very special maintenance conditions. These plans include the definition of priority schemes to start the distribution process and, since it is very likely that not all people will be vaccinated for different
Food webs are complex networks describing trophic interactions in ecological communities. Since R... more Food webs are complex networks describing trophic interactions in ecological communities. Since Robert May's seminal work on random structured food webs, the complexity-stability debate is a central issue in ecology: does network complexity increase or decrease food-web persistence? A multi-species predator-prey model incorporating adaptive predation shows that the action of ecological dynamics on the topology of a food web (whose initial configuration is generated either by the cascade model or by the niche model) render, when a significant fraction of adaptive predators is present, similar hyperbolic complexity-persistence relationships as those observed in empirical food webs. It is also shown that the apparent positive relation between complexity and persistence in food webs generated under the cascade model, which has been pointed out in previous papers, disappears when the final connectance is used instead of the initial one to explain species persistence.
The emergence of uncorrelated growing networks is proved when nodes are removed either uniformly ... more The emergence of uncorrelated growing networks is proved when nodes are removed either uniformly or under the preferential survival rule recently observed in the WWW evolution. To this aim the rate equation for the joint probability of degrees is derived and stationary symmetrical solutions are obtained by passing to the continuum limit. When uniformly random removal of extant nodes and linear preferential attachment of new nodes are at work, we obtain that the only stationary solution corresponds to uncorrelated networks for any removal rate r ∈ [0, 1). In the more general case of preferential survival of nodes, uncorrelated solutions are also obtained. These results generalize the uncorrelatedness displayed by the (undirected) Barabási-Albert network model to models with uniformly random and selective (against low degrees) removal of nodes.
We study ODE models of epidemic spreading with a preventive behavioral response that is triggered... more We study ODE models of epidemic spreading with a preventive behavioral response that is triggered by awareness of the infection. Previous studies of such models have mostly focused on the impact of the response on the initial growth of an outbreak and the existence and location of endemic equilibria. Here we study the question whether this type of response is sufficient to prevent future flare-ups from low endemic levels if awareness is assumed to decay over time. In the ODE context, such flare-ups would translate into sustained oscillations with significant amplitudes. Our results show that such oscillations are ruled out in Susceptible-Aware-Infectious-Susceptible models with a single compartment of aware hosts, but can occur if we consider two distinct compartments of aware hosts who differ in their willingness to alert other susceptible hosts.
To improve the accuracy of network-based SIS models we introduce and study a multilayer represent... more To improve the accuracy of network-based SIS models we introduce and study a multilayer representation of a time-dependent network. In particular, we assume that individuals have their long-term (permanent) contacts that are always present, identifying in this way the first network layer. A second network layer also exists, where the same set of nodes can be connected by occasional links, created with a given probability. While links of the first layer are permanent, a link of the second layer is only activated with some probability and under the condition that the two nodes, connected by this link, are simultaneously participating to the temporary link. We develop a model for the SIS epidemic on this time-dependent network, analyze equilibrium and stability of the corresponding mean-field equations, and shed some light on the role of the temporal layer on the spreading process.
In this paper we study the appearance of bifurcations of limit cycles in an epidemic model with t... more In this paper we study the appearance of bifurcations of limit cycles in an epidemic model with two types of aware individuals. All the transition rates are constant except for the alerting decay rate of the most aware individuals and the rate of creation of the less aware individuals, which depend on the disease prevalence in a non-linear way. For the ODE model, the numerical computation of the limit cycles and the study of their stability are made by means of the Poincaré map. Moreover, sufficient conditions for the existence of an endemic equilibrium are also obtained. These conditions involve a rather natural relationship between the transmissibility of the disease and that of awareness. Finally, stochastic simulations of the model under a very low rate of imported cases are used to confirm the scenarios of bistability (endemic equilibrium and limit cycle) observed in the solutions of the ODE model.
Systems with many components (individuals or local populations as cities, or metropolitan areas, ... more Systems with many components (individuals or local populations as cities, or metropolitan areas, or regions, …) connected by non-trivial associations or relationships can be statistically described by means of the formalism of complex networks which is based on descriptors like degree distributions, degree-degree correlations, etc. In the last years, many researchers from different fields have been using different approaches to model processes taking place on complex networks.
We present a pair-approximation model for spatial forest dynamics defined on a regular lattice. T... more We present a pair-approximation model for spatial forest dynamics defined on a regular lattice. The model assumes three possible states for a lattice site: empty (gap site), occupied by an immature tree, and occupied by a mature tree, and considers three nonlinearities in the dynamics associated to the processes of light interference, gap expansion, and recruitment. We obtain an expression of the basic reproduction number R(0) which, in contrast to the one obtained under the mean-field approach, uses information about the spatial arrangement of individuals close to extinction. Moreover, we analyze the corresponding survival-extinction transition of the forest and the spatial correlations among gaps, immature and mature trees close to this critical point. Predictions of the pair-approximation model are compared with those of a cellular automaton.
We present the derivation of the continuous-time equations governing the limit dynamics of discre... more We present the derivation of the continuous-time equations governing the limit dynamics of discrete-time reaction-diffusion processes defined on heterogeneous metapopulations. We show that, when a rigorous time limit is performed, the lack of an epidemic threshold in the spread of infections is not limited to metapopulations with a scale-free architecture, as it has been predicted from dynamical equations in which reaction and diffusion occur sequentially in time.
After a presentation of the paper cited above at a workshop on Dynamic Networks at the Isaac Newt... more After a presentation of the paper cited above at a workshop on Dynamic Networks at the Isaac Newton Institute for Mathematical Sciences, Cambridge, prof Frank Ball in discussions explained two potential errors in our analysis. After further discussions this was indeed confirmed. One mistake was an oversight, whereas the second one was more subtle. It turns out that the first mistake has impacts on the results of the paper, whereas the second one can be repaired and hence has no effect on the results. The oversight appears in Section 4.1 where the basic reproduction number R BA
The Markovian approach, which assumes exponentially distributed interinfection times, is dominant... more The Markovian approach, which assumes exponentially distributed interinfection times, is dominant in epidemic modeling. However, this assumption is unrealistic as an individual's infectiousness depends on its viral load and varies over time. In this paper, we present a Susceptible-Infected-Recovered-Vaccinated-Susceptible epidemic model incorporating non-Markovian infection processes. The model can be easily adapted to accurately capture the generation time distributions of emerging infectious diseases, which is essential for accurate epidemic prediction. We observe noticeable variations in the transient behavior under different infectiousness profiles and the same basic reproduction number R0. The theoretical analyses show that only R0 and the mean immunity period of the vaccinated individuals have an impact on the critical vaccination rate needed to achieve herd immunity. A vaccination level at the critical vaccination rate can ensure a very low incidence among the population in the case of future epidemics, regardless of the infectiousness profiles.
This paper is concerned with the robustness of the sustained oscillations predicted by an epidemi... more This paper is concerned with the robustness of the sustained oscillations predicted by an epidemic ODE model defined on contact networks. The model incorporates the spread of awareness among individuals and, moreover, a small inflow of imported cases. These cases prevent stochastic extinctions when we simulate the epidemics and, hence, they allow to check whether the average dynamics for the fraction of infected individuals are accurately predicted by the ODE model. Stochastic simulations confirm the existence of sustained oscillations for different types of random networks, with a sharp transition from a non-oscillatory asymptotic regime to a periodic one as the alerting rate of susceptible individuals increases from very small values. This abrupt transition to periodic epidemics of high amplitude is quite accurately predicted by the Hopf-bifurcation curve computed from the ODE model using the alerting rate and the infection transmission rate for aware individuals as tuning parameters.
This paper is concerned with stochastic SIR and SEIR epidemic models on random networks in which ... more This paper is concerned with stochastic SIR and SEIR epidemic models on random networks in which individuals may rewire away from infected neighbors at some rate ω (and reconnect to non-infectious individuals with probability α or else simply drop the edge if α = 0), so-called preventive rewiring. The models are denoted SIR-ω and SEIR-ω, and we focus attention on the early stages of an outbreak, where we derive expression for the basic reproduction number R 0 and the expected degree of the infectious nodes E(D I) using two different approximation approaches. The first approach approximates the early spread of an epidemic by a branching process, whereas the second one uses pair approximation. The expressions are compared with the corresponding empirical means obtained from stochastic simulations of SIR-ω and SEIRω epidemics on Poisson and scale-free networks. Without rewiring of exposed nodes, the two approaches predict the same epidemic threshold and the same E(D I) for both types of epidemics, the latter being very close to the mean degree obtained from simulated epidemics over Poisson networks. Above the epidemic threshold, pairwise models overestimate the value of R 0 computed from simulations, which turns out to be very close to the one predicted by the branching process approximation. When exposed individuals also rewire with α > 0 (perhaps unaware of being infected), the two approaches give different epidemic thresholds, with the branching process approximation being more in agreement with simulations.
Using a bioenergetic model we show that the pattern of foraging preferences greatly determines th... more Using a bioenergetic model we show that the pattern of foraging preferences greatly determines the complexity of the resulting food webs. By complexity we refer to the degree of richness of food‐web architecture, measured in terms of some topological indicators (number of persistent species and links, connectance, link density, number of trophic levels, and frequency of weak links). The poorest food‐web architecture is found for a mean‐field scenario where all foraging preferences are assumed to be the same. Richer food webs appear when foraging preferences depend on the trophic position of species. Food‐web complexity increases with the number of basal species. We also find a strong correlation between the complexity of a trophic module and the complexity of entire food webs with the same pattern of foraging preferences.
The structural properties of the subway network are crucial in effective transportation in cities... more The structural properties of the subway network are crucial in effective transportation in cities. This paper presents an information perspective of navigation in four different subway networks: New York City, Paris, Barcelona and Moscow. We addressed our study to investigate what is that makes it complicated to navigate in these kinds of networks and we carried out a comparison between them and their intrinsic constraints. Our methodological approach is based on a set of cost/efficiency indicators which are defined in the complex networks literature. We find that the overall complexity in finding stations measured by the average search information S linearly increases as a function of the network size N. The direct implication of this finding is that from these basic levels of required information, the average value H(k) can be represented as a function of the node degree k. Finally, through analyzing subway networks in space P, we reveal the existing service modularity among subway routes using a rescaled expression of S.
We present a continuum formalism for modeling growing random networks under addition and deletion... more We present a continuum formalism for modeling growing random networks under addition and deletion of nodes based on a differential mass balance equation. As examples of its applicability, we obtain new results on the degree distribution for growing networks with a uniform attachment and deletion of nodes, and complete some recent results on growing networks with preferential attachment and uniform removal.
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service... more This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Currently, several western countries have more than half of their population fully vaccinated aga... more Currently, several western countries have more than half of their population fully vaccinated against COVID-19. At the same time, some of them are experiencing a fourth or even a fifth wave of cases, most of them concentrated in sectors of the populations whose vaccination coverage is lower than the average. So, the initial scenario of vaccine prioritization has given way to a new one where achieving herd immunity is the primary concern. Using an age-structured vaccination model with waning immunity, we show that, under a limited supply of vaccines, a vaccination strategy based on minimizing the basic reproduction number allows for the deployment of a number of vaccine doses lower than the one required for maximizing the vaccination coverage. Such minimization is achieved by giving greater protection to those age groups that, for a given social contact pattern, have smaller fractions of susceptible individuals at the endemic equilibrium without vaccination, that is, to those groups that are more vulnerable to infection. The pandemic of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is still imposing incredible pressure on many countries' healthcare and economic systems. Nations in America, Europe, Asia, and Africa have faced large numbers of deaths due to COVID 19, and a continued crisis situation. The only good news in this dark situation is that vaccines are becoming available from different companies all over the world. Some countries are currently evaluating the efficacy and effectiveness of developed vaccines, while some other countries have already started their vaccination campaign. In particular, as of November 2021, more than 75% of the people in countries like Canada, United Kingdom, and France have received at least one dose of the vaccination, while no more than 35% of people in Bangladesh, Guinea, and Armenia have received one dose at least 1. These examples give an idea of the heterogeneous situation of the vaccination campaign in the world. Additionally, current studies suggest a decay of neutralizing antibody responses in convalescent patients 2 , as well as a decline in the effectiveness of mRNA COVID-19 vaccines 3. Therefore, vaccines probably provide a short-lived immunity. For instance, comparing the rate of decay of the antibody responses following infections by human coronavirus (hCoV) and by SARS-CoV-2, it has been suggested that individuals may become susceptible to reinfection within 12-18 months after a previous infection 2. Similarly, a recent comparative evolutionary analysis of coronavirus relatives of SRAS-CoV-2 reveals that, under endemic conditions, reinfection by SARS-CoV-2 would likely occur between 3 months and 5.1 years after peak antibody response, with a median of 16 months 4. While during the ongoing pandemic most countries agree to vaccinate first public health personnel and people in long term care facilities, the limited availability of vaccines and the logistic complexities are still posing big questions on when and how the vaccination campaign will be completed. Initially, some countries assessed reaching herd immunity at around 70% of the population vaccinated 5. With time, several hurdles upon this achievement are becoming evident 6. These difficulties in obtaining herd immunity may further discouraging people from attaining it 5. Countries are now developing immunization plans to face the challenge of distributing millions of vaccines, some of which require very special maintenance conditions. These plans include the definition of priority schemes to start the distribution process and, since it is very likely that not all people will be vaccinated for different
Food webs are complex networks describing trophic interactions in ecological communities. Since R... more Food webs are complex networks describing trophic interactions in ecological communities. Since Robert May's seminal work on random structured food webs, the complexity-stability debate is a central issue in ecology: does network complexity increase or decrease food-web persistence? A multi-species predator-prey model incorporating adaptive predation shows that the action of ecological dynamics on the topology of a food web (whose initial configuration is generated either by the cascade model or by the niche model) render, when a significant fraction of adaptive predators is present, similar hyperbolic complexity-persistence relationships as those observed in empirical food webs. It is also shown that the apparent positive relation between complexity and persistence in food webs generated under the cascade model, which has been pointed out in previous papers, disappears when the final connectance is used instead of the initial one to explain species persistence.
The emergence of uncorrelated growing networks is proved when nodes are removed either uniformly ... more The emergence of uncorrelated growing networks is proved when nodes are removed either uniformly or under the preferential survival rule recently observed in the WWW evolution. To this aim the rate equation for the joint probability of degrees is derived and stationary symmetrical solutions are obtained by passing to the continuum limit. When uniformly random removal of extant nodes and linear preferential attachment of new nodes are at work, we obtain that the only stationary solution corresponds to uncorrelated networks for any removal rate r ∈ [0, 1). In the more general case of preferential survival of nodes, uncorrelated solutions are also obtained. These results generalize the uncorrelatedness displayed by the (undirected) Barabási-Albert network model to models with uniformly random and selective (against low degrees) removal of nodes.
We study ODE models of epidemic spreading with a preventive behavioral response that is triggered... more We study ODE models of epidemic spreading with a preventive behavioral response that is triggered by awareness of the infection. Previous studies of such models have mostly focused on the impact of the response on the initial growth of an outbreak and the existence and location of endemic equilibria. Here we study the question whether this type of response is sufficient to prevent future flare-ups from low endemic levels if awareness is assumed to decay over time. In the ODE context, such flare-ups would translate into sustained oscillations with significant amplitudes. Our results show that such oscillations are ruled out in Susceptible-Aware-Infectious-Susceptible models with a single compartment of aware hosts, but can occur if we consider two distinct compartments of aware hosts who differ in their willingness to alert other susceptible hosts.
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Papers by Joan Saldana