Related papers: Effective edge-based approach for promoting the sp…
We introduce a stochastic SIR-type partial differential equation model incorporating random diffusion, reinfection, vital dynamics, and a randomly varying transmission rate. For the associated random dynamical system, we prove the existence…
Drug resistance and strong contacts actually play crucial roles in epidemic spread in complex systems. Nevertheless, neither theoretical model or methodology is proposed to address this. We thus consider an edge-based epidemic spread model…
In this paper, we develop a node-based approximate model for Markovian contagion dynamics on networks. We prove that our approximate model is exact for SIR (susceptible-infectious-recovered) and SEIR…
We study the spread of stochastic SIR (Susceptible $\to$ Infectious $\to$ Recovered) epidemics in two types of structured populations, both consisting of schools and households. In each of the types, every individual is part of one school…
In this study, we present an integro-differential model to simulate the local spread of infections. The model incorporates a standard susceptible-infected-recovered (\textit{SIR}-) model enhanced by an integral kernel, allowing for…
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…
The basic Susceptible-Infected-Recovered (SIR) model is extended to include effects of progressive social awareness, lockdowns and anthropogenic migration. It is found that social awareness can effectively contain the spread by lowering the…
Motivated by scenarios of epidemic competition, as well as how social contagions spread at the level of individuals, this work considers the competition between two conflicting node states that spread over a social graph according to a…
In this chapter, we consider the problem of designing protection strategies to contain spreading processes in complex cyber-physical networks. We illustrate our ideas using a family of bio-motivated spreading models originally proposed in…
We study the dynamics of secondary infections on networks, in which only the individuals currently carrying a certain primary infection are susceptible to the secondary infection. In the limit of large sparse networks, the model is mapped…
Containment of epidemic outbreaks entails great societal and economic costs. Cost-effective containment strategies rely on efficiently identifying infected individuals, making the best possible use of the available testing resources.…
We study two simple mathematical models of the epidemic. At first, we study the repetitive infection spreading in a simplified SIRS model including the effect of the decay of the acquired immune. The model is an intermediate model of the…
In this paper we study a discrete-time SIS (susceptible-infected-susceptible) model, where the infection and healing parameters and the underlying network may change over time. We provide conditions for the model to be well-defined and…
Even though transitivity is a central structural feature of social networks, its influence on epidemic spread on coevolving networks has remained relatively unexplored. Here we introduce and study an adaptive SIS epidemic model wherein the…
This paper presents a novel time-space SIR (Susceptible-Infected-Recovered) model for simulating infectious disease dynamics in two interconnected regions. The model is formulated as a coupled reaction-diffusion system with boundary…
Network epidemiology has become a vital tool in understanding the effects of high-degree vertices, geographic and demographic communities, and other inhomogeneities in social structure on the spread of disease. However, many networks…
Most epidemic models assume equal mixing among members of a population. An alternative approach is to model a population as random network in which individuals may have heterogeneous connectivity. This paper builds on previous research by…
In social networks, control of rumor spread is an active area of research. SIR model is generally used to study the rumor dynamics in network while considering the rumor as an epidemic. In disease spreading model, epidemic is controlled by…
The Susceptible-Infected-Susceptible model is a canonical model for emerging disease outbreaks. Such outbreaks are naturally modeled as taking place on networks. A theoretical challenge in network epidemiology is the dynamic correlations…
Various kinds of spread of influence occur in real world social and virtual networks. These phenomena are formulated by activation processes and irreversible dynamic monopolies in combinatorial graphs representing the topology of the…