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In contrast to the common assumption in epidemic models that the rate of infection between individuals is constant, in reality, an individual's viral load determines their infectiousness. We compare the average and individual reproductive…
Neuronal voltage dynamics of regularly firing neurons typically has one stable attractor: either a fixed point (like in the subthreshold regime) or a limit cycle that defines the tonic firing of action potentials (in the suprathreshold…
The existence and local stability of some non-negative equilibrium points of a class of SIRS infectious disease models with non-linear infection and treatment rates are investigated under the condition that the total population is a…
Social reinforcement mechanism, which characterizes the promoting effects when exposing to multiple sources in social contagion process, is ubiquitous in information-technology ecosystem and has aroused great attention in recent years.…
An epidemic Susceptible-Vaccinated-Infected-Removed-Susceptible (SVIRS) model is presented on a weighted-undirected network with graph Laplacian diffusion. Disease-free equilibrium always exists while the existence and uniqueness of endemic…
This paper conducts research on the established model and presents the main conclusions . Firstly, by separately considering the infectivity of each of the two infectious diseases and the infectivity of the population simultaneously…
We propose two SIR models which incorporate sociological behavior of groups of individuals. It is these differences in behaviors which impose different infection rates on the individual susceptible populations, rather than biological…
We present and analyze a mathematical model to study the feedback between behavior and epidemic spread in a population that is actively assessing and reacting to risk of infection. In our model, a population dynamically forms an opinion…
The compartmental models used to study epidemic spreading often assume the same susceptibility for all individuals, and are therefore, agnostic about the effects that differences in susceptibility can have on epidemic spreading. Here we…
In the real world, many complex systems interact with other systems. In addition, the intra- or inter-systems for the spread of information about infectious diseases and the transmission of infectious diseases are often not random, but with…
In this work, we aim to understand the influence of the heterogeneity of infection rates on the Susceptible-Infected-Susceptible (SIS) epidemic spreading. Employing the classic SIS model as the benchmark, we study the influence of the…
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…
The duration, type and structure of connections between individuals in real-world populations play a crucial role in how diseases invade and spread. Here, we incorporate the aforementioned heterogeneities into a model by considering a…
Epilepsy is one of the most common neurological disorders globally, affecting millions of individuals. Despite significant advancements, the precise mechanisms underlying this condition remain largely unknown, making accurately predicting…
Motivated by fundamental issues in non-equilibrium statistical mechanics (NESM), we study the venerable susceptible-infected (SIS) model of disease spreading in an idealized, simple setting. Using Monte Carlo and analytic techniques, we…
Disease awareness in epidemiology can be modelled with adaptive contact networks, where the interplay of disease dynamics and network alteration often adds new phases to the standard models (Gross et al. 2006, Shaw et al. 2008) and, in…
In this paper, dynamical systems theory and bifurcation theory are applied to investi- gate the rich dynamical behaviours observed in three simple disease models. The 2- and 3-dimensional models we investigate have arisen in previous…
The focus of this article is on the dynamics of a new susceptible-infected model which consists of a susceptible group ($S$) and two different infectious groups ($I_1$ and $I_2$). Once infected, an individual becomes a member of one of…
In recent years, classical epidemic models, which assume stationary behavior of individuals, have been extended to include an adaptive heterogeneous response of the population to the current state of the epidemic. However, it is widely…
We study the stability properties of a susceptible-infected-susceptible (SIS) diffusion model, so-called the $n$-intertwined Markov model, over arbitrary directed network topologies. As in the majority of the work on infection spread…