arXiv subjects

L. G. Alvarez-Zuzek

Publications and source records attributed to L. G. Alvarez-Zuzek.

4 recordsLinked to original sources

arXiv2019

Dynamic vaccination in partially overlapped multiplex network

In this work we propose and investigate a new strategy of vaccination, which we call "dynamic vaccination". In our model, susceptible people become aware that one or more of their contacts are infected, and thereby get vaccinated with probability $ω$, before having physical contact with any infected patient. Then, the non-vaccinated individuals will be infected with probability $β$. We apply the strategy to the SIR epidemic model in a multiplex network composed by two networks, where a fraction $q$ of the nodes acts in both networks. We map this model of dynamic vaccination into bond percolation model, and use the generating functions framework to predict theoretically the behavior of the relevant magnitudes of the system at the steady state. We find a perfect agreement between the solutions of the theoretical equations and the results of stochastic simulations. In addition, we find an interesting phase diagram in the plane $β-ω$, which is composed by an epidemic and a non-epidemic phases, separated by a critical threshold line $β_c$, which depends on $q$. Wefind that, for all values of $q$, a region in the diagram where the vaccination is so efficient that, regardless of the virulence of the disease, it never becomes an epidemic. We compare our strategy with random immunization and find that using the same amount of vaccines for both scenarios, we obtain that the spread of the disease is much lower in the case of dynamic vaccination when compared to random immunization. Furthermore, we also compare our strategy with targeted immunization and we find that, depending on $ω$, dynamic vaccination will perform significantly better, and in some cases will stop the disease before it becomes an epidemic.

physics.soc-ph↗

arXiv2018

Multiple outbreaks in epidemic spreading with local vaccination and limited vaccines

How to prevent the spread of human diseases is a great challenge for the scientific community and so far there are many studies in which immunization strategies have been developed. However, these kind of strategies usually do not consider that medical institutes may have limited vaccine resources available. In this manuscript, we explore the Susceptible-Infected-Recovered (SIR) model with local dynamic vaccination, and considering limited vaccines. In this model, susceptibles in contact with an infected individual, are vaccinated -with probability $ω$- and then get infected -with probability $β$. However, when the fraction of immunized individuals reaches a threshold $V_L$, the vaccination stops, after which only the infection is possible. In the steady state, besides the critical points $β_c$ and $ω_c$ that separate a non-epidemic from an epidemic phase, we find for a range of $V_L$ another transition points, $β^*>β_c$ and $ω^*<ω_c$, which correspond to a novel discontinuous phase transition. This critical value separates a phase where the amount of vaccines is sufficient, from a phase where the disease is strong enough to exhaust all the vaccination units. For a disease with fixed $β$, the vaccination probability $ω$ can be controlled in order to drastically reduce the number of infected individuals, using efficiently the available vaccines. Furthermore, the temporal evolution of the system close to $β^*$ or $ω^*$, shows that after a peak of infection the system enters into a quasi-stationary state, with only a few infected cases. But if there are no more vaccines, these few infected individuals could originate a second outbreak, represented by a second peak of infection. This state of apparent calm, could be dangerous since it may lead to misleading conclusions and to an abandon of the strategies to control the disease.

physics.soc-ph↗

arXiv2017

Epidemic spreading in multiplex networks influenced by opinion exchanges on vaccination

We study the changes of opinions about vaccination together with the evolution of a disease. In our model we consider a multiplex network consisting of two layers. One of the layers corresponds to a social network where people share their opinions and influence others opinions. The social model that rules the dynamic is the M-model, which takes into account two different processes that occurs in a society: persuasion and compromise. This two processes are related through a parameter $r$, $r<1$ describes a moderate and committed society, for $r>1$ the society tends to have extremist opinions, while $r=1$ represents a neutral society. This social network may be of real or virtual contacts. On the other hand, the second layer corresponds to a network of physical contacts where the disease spreading is described by the SIR-Model. In this model the individuals may be in one of the following four states: Susceptible ($S$), Infected($I$), Recovered ($R$) or Vaccinated ($V$). A Susceptible individual can: i) get vaccinated, if his opinion in the other layer is totally in favor of the vaccine, ii) get infected, with probability $β$ if he is in contact with an infected neighbor. Those $I$ individuals recover after a certain period $t_r=6$. Vaccinated individuals have an extremist positive opinion that does not change. We consider that the vaccine has a certain effectiveness $ω$ and as a consequence vaccinated nodes can be infected with probability $β(1 - ω)$ if they are in contact with an infected neighbor. In this case, if the infection process is successful, the new infected individual changes his opinion from extremist positive to totally against the vaccine. We find that depending on the trend in the opinion of the society, which depends on $r$, different behaviors in the spread of the epidemic occurs. An epidemic threshold was found.

physics.soc-ph↗

arXiv2016

Interacting social processes on interconnected networks

We propose and study a model for the interplay between two different dynamical processes --one for opinion formation and the other for decision making-- on two interconnected networks $A$ and $B$. The opinion dynamics on network $A$ corresponds to that of the M-model, where the state of each agent can take one of four possible values ($S=-2,-1,1,2$), describing its level of agreement on a given issue. The likelihood to become an extremist ($S=\pm 2$) or a moderate ($S=\pm 1$) is controlled by a reinforcement parameter $r \ge 0$. The decision making dynamics on network $B$ is akin to that of the Abrams-Strogatz model, where agents can be either in favor ($S=+1$) or against ($S=-1$) the issue. The probability that an agent changes its state is proportional to the fraction of neighbors that hold the opposite state raised to a power $β$. Starting from a polarized case scenario in which all agents of network $A$ hold positive orientations while all agents of network $B$ have a negative orientation, we explore the conditions under which one of the dynamics prevails over the other, imposing its initial orientation. We find that, for a given value of $β$, the two-network system reaches a consensus in the positive state (initial state of network $A$) when the reinforcement overcomes a crossover value $r^*(β)$, while a negative consensus happens for $r β_c$. We develop an analytical mean-field approach that gives an insight into these regimes and shows that both dynamics are equivalent along the crossover line $(r^*,β^*)$.

physics.soc-ph↗