相关论文: Bivariate collocation for computing $R_{0}$ in epi…
Degree correlation plays a crucial role in studying network structures; however, its varied forms pose challenges to understanding its impact on network dynamics. This study devised a method that uses eigenvalue decomposition to…
In this paper, we propose a realistic mathematical model taking into account the mutual interference among the interacting populations. This model attempts to describe the control (vaccination) function as a function of the number of…
Accurate and reliable forecasting of epidemic incidences is critical for public health preparedness, yet it remains a challenging task due to complex nonlinear temporal dependencies and heterogeneous spatial interactions. Often, point…
The abrupt outbreak and transmission of biological diseases has always been a long-time concern of humankind. For long, mathematical modeling has served as a simple and yet efficient tool to investigate, predict, and control spread of…
This paper introduces a novel hybrid model combining Partial Differential Equations (PDEs) and Ordinary Differential Equations (ODEs) to simulate infectious disease dynamics across geographic regions. By leveraging the spatial detail of…
Spatio-temporal extensions of familiar compartment models for disease transmission incorporating diffusive behavior, or interactions between individuals at separate locations, are explored. The models considered have the character of…
In this paper we first introduce the general stochastic epidemic model for the spread of infectious diseases. Then we give methods for inferring model parameters such as the basic reproduction number $R_0$ and vaccination coverage $v_c$…
Motile organisms can form stable agglomerates such as cities or colonies. In the outbreak of a highly contagious disease, the control of large-scale epidemic spread depends on factors like the number and size of agglomerates, travel rate…
Motivated by analogies between the spreading of human-to-human infections and of chemical processes, we develop a comprehensive model that accounts both for infection and for transport. In this analogy, the three different populations of…
Compartmental models are valuable tools for investigating infectious diseases. Researchers building such models typically begin with a simple structure where compartments correspond to individuals with different epidemiological statuses,…
We consider the edge-based compartmental models for infectious disease spread introduced in Part I. These models allow us to consider standard SIR diseases spreading in random populations. In this paper we show how to handle deviations of…
Background: Recently developed techniques to study the spread of infectious diseases through networks make assumptions that the initial proportion infected is infinitesimal and the population behavior is static throughout the epidemic. The…
A social (sexual) network is modeled by an extension of the configuration model to the situation where edges have weights, e.g. reflecting the number of sex-contacts between the individuals. An epidemic model is defined on the network such…
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…
Most of the common used models of epidemic spreading allow contaminating many neighbors of a particular node in the network. They are usually analyzed by differential equations on probability vectors. We propose a model of epidemic…
We study the stochastic susceptible-infected-susceptible model of epidemic processes on finite directed and weighted networks with arbitrary structure. We present a new lower bound on the exponential rate at which the probabilities of nodes…
We present a generic epidemic model with stochastic parameters, in which the dynamics self-organize to a critical state with suppressed exponential growth. More precisely, the dynamics evolve into a quasi-steady-state, where the effective…
In recent years, spatial and spatio-temporal modeling have become an important area of research in many fields (epidemiology, environmental studies, disease mapping). In this work we propose different spatial models to study hospital…
This work provides a geometric version of the next-generation matrix method for obtaining the basic reproduction number of an epidemiological model. We exhibit a certain correspondence between any system of ODEs and Petri nets. We observe…
Epidemic models are used to analyze the progression or outcome of an epidemic under different control policies like vaccinations, quarantines, lockdowns, use of face-masks, pharmaceutical interventions, etc. When these models accurately…