Multiple outbreaks in epidemic spreading with local vaccination and limited vaccines

Abstract

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 $\omega$- and then get infected -with probability $\beta$. 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 ${\beta }_c$ and ${\omega }_c$ that separate a non-epidemic from an epidemic phase, we find for a range of $V_L$ another transition points, ${\beta }^{\ast }>{\beta }_c$ and ${\omega }^{\ast }<{\omega }_c$, 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 $\beta$, the vaccination probability $\omega$ 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 ${\beta }^{\ast }$ or ${\omega }^{\ast }$, 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.

References in corpus (15)

• Understanding individual human mobility patterns
• Prediction and predictability of global epidemics: the role of the airline transportation network
• Efficient Immunization Strategies for Computer Networks and Populations
• Statistical physics of vaccination
• Dynamics of person-to-person interactions from distributed RFID sensor networks
• Thresholds for epidemic spreading in networks
• Unification of theoretical approaches for epidemic spreading on complex networks
• Improving immunization strategies
• Spreading of sexually transmitted diseases in heterosexual populations
• Optimal Deployment of Resources for Maximizing Impact in Spreading Processes
• Epidemic Model with Isolation in Multilayer Networks
• Immunization strategy for epidemic spreading on multilayer networks
• Estimating the value of containment strategies in delaying the arrival time of an influenza pandemic: A case study of travel restriction and patient isolation
• Interacting opinion and disease dynamics in multiplex networks: discontinuous phase transition and non-monotonic consensus times
• Temporal percolation of the susceptible network in an epidemic spreading

Cited by in corpus (9)

• Criticality in spreading processes without time-scale separation and the critical brain hypothesis
• Social contagions with communication channels alternation on multiplex networks
• Containing misinformation spreading in temporal social networks
• Discontinuous epidemic transition due to limited testing
• Disease spreading with social distancing: A prevention strategy in disordered multiplex networks
• Containing rumors spreading on correlated multiplex networks
• Transition from Susceptible-Infected to Susceptible-Infected-Recovered Dynamics in a Susceptible-Cleric-Zombie-Recovered Active Matter Model
• Superexponential growth of epidemics in networks with cliques
• Modeling Epidemic Dynamics of Mutant Strains with Evolutionary Game-based Vaccination Behavior