Related papers: Spreading processes in "post-epidemic" environment…
Transportation networks play a critical part in the spread of infectious diseases between populations. In this work, we define a networked susceptible-exposed-infected-recovered epidemic process with loss of immunity over time (SEIRS) that…
One of the popular dynamics on complex networks is the epidemic spreading. An epidemic model describes how infections spread throughout a network. Among the compartmental models used to describe epidemics, the…
We investigate the spread of diseases, computer viruses or information on complex networks and also immunization strategies to prevent or control the spread. When an entire population cannot be immunized and the effect of immunization is…
Contagious processes, such as spread of infectious diseases, social behaviors, or computer viruses, affect biological, social, and technological systems. Epidemic models for large populations and finite populations on networks have been…
We study the classic Susceptible-Infected-Recovered (SIR) model for the spread of an infectious disease. In this stochastic process, there are two competing mechanism: infection and recovery. Susceptible individuals may contract the disease…
We study spreading processes in two-dimensional systems of heterogeneous active agents that exhibit different individual active speeds. We obtain, combining kinetic and complex network theory, an analytical expression for the spreading…
Susceptible-Infected-Recovered (SIR) models have been used for decades to understand epidemic outbreak dynamics. We develop an SIR model specifically designed to study the effects of population behavior with respect to health and…
In this paper we study the diffusion of an SIS-type epidemics on a network under the presence of a random environment, that enters in the definition of the infection rates of the nodes. Accordingly, we model the infection rates in the form…
This paper examines a susceptible-infected-susceptible (SIS) epidemic reaction-diffusion model with no-flux boundary conditions and constant total population. The infection mechanism in the model is described by a nonlinear term of the form…
We study the spreading of an infection within an SIS epidemiological model on a network. Susceptible agents are given the opportunity of breaking their links with infected agents. Broken links are either permanently removed or reconnected…
We study the diffusion of epidemics on networks that are partitioned into local communities. The gross structure of hierarchical networks of this kind can be described by a quotient graph. The rationale of this approach is that individuals…
The spreading of infectious diseases with and without immunization of individuals can be modeled by stochastic processes that exhibit a transition between an active phase of epidemic spreading and an absorbing phase, where the disease dies…
In this paper, we present stochastic synchronous cellular automaton defined on a square lattice. The automaton rules are based on the SEIR (susceptible $\to$ exposed $\to$ infected $\to$ recovered) model with probabilistic parameters…
We formulate a generalized susceptible exposed infectious recovered (SEIR) model on a graph, describing the population dynamics of an open crowded place with an arbitrary topology. As a sample calculation, we discuss three simple cases,…
The waning of immunity after recovery or vaccination is a major factor accounting for the severity and prolonged duration of an array of epidemics, ranging from COVID-19 to diphtheria and pertussis. To study the effectiveness of different…
The dynamics of contact networks and epidemics of infectious diseases often occur on comparable time scales. Ignoring one of these time scales may provide an incomplete understanding of the population dynamics of the infection process. We…
The current survey paper concerns stochastic mathematical models for the spread of infectious diseases. It starts with the simplest setting of a homogeneous population in which a transmittable disease spreads during a short outbreak.…
We study the Susceptible-Infectious-Susceptible (SIS) model on arbitrary networks. The well-established pair approximation treats neighboring pairs of nodes exactly while making a mean field approximation for the rest of the network. We…
For many infectious diseases, a small-world network on an underlying regular lattice is a suitable simplified model for the contact structure of the host population. It is well known that the contact network, described in this setting by a…
Optimal strategies for epidemic containment are focused on dismantling the contact network through effective immunization with minimal costs. However, network fragmentation is seldom accessible in practice and may present extreme side…