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In this work we propose a novel space-dependent multiscale model for the spread of infectious diseases in a two-dimensional spatial context on realistic geographical scenarios. The model couples a system of kinetic transport equations…
We introduce an agent-based model for the spreading of technological developments in socio-economic systems where the technology is mainly used for the collaboration/interaction of agents. Agents use products of different technologies to…
A simplified susceptible-infected-recovered (SIR) epidemic model and a small-world model are applied to analyse the spread and control of Severe Acute Respiratory Syndrome (SARS) for Hong Kong in early 2003. From data available in mid April…
Multidimensional continuous-time Markov jump processes $(Z(t))$ on $\mathbb{Z}^p$ form a usual set-up for modeling $SIR$-like epidemics. However, when facing incomplete epidemic data, inference based on $(Z(t))$ is not easy to be achieved.…
Throughout the course of an epidemic, the rate at which disease spreads varies with behavioral changes, the emergence of new disease variants, and the introduction of mitigation policies. Estimating such changes in transmission rates can…
In network-based SIS models of infectious disease transmission, infection can only occur between directly connected individuals. This constraint naturally gives rise to spatial correlations between the states of neighboring nodes, as the…
This paper examines an epidemic patch model with mass-action transmission mechanism and asymmetric connectivity matrix. Results on the global dynamics of solutions and the spatial structures of endemic solutions are obtained. In particular,…
Viral kinetics have been extensively studied in the past through the use of spatially well-mixed ordinary differential equations describing the time evolution of the diseased state. However, emerging spatial structures such as localized…
We investigate an epidemic model based on Bailey's continuous differential system. In the continuous time domain, we extend the classical model to time-dependent coefficients and present an alternative solution method to Gleissner's…
We introduce a modified SIR model with memory for the dynamics of epidemic spreading in a constant population of individuals. Each individual is in one of the states susceptible (${\bf S}$), infected (${\bf I}$) or recovered (${\bf R}$). In…
In this research, we study the propagation patterns of epidemic diseases such as the COVID-19 coronavirus, from a mathematical modeling perspective. The study is based on an extensions of the well-known susceptible-infected-recovered (SIR)…
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…
This paper presents a discrete time probabilistic dynamic for simulating a contact-based epidemic spreading based on discrete time Markov chain process, in particular the attention is addressed to the susceptible-infectious-removed (SIR)…
We study an infection-age structured epidemic model in which both the infectivity and the rate of loss of immunity depend on the time-since-infection. The model can be equivalently viewed as a nonlinear renewal equation for the incidence of…
With the outbreak of COVID-19, how to mitigate and suppress its spread is a big issue to the government. Department of public health need powerful models to model and predict the trend and scale of such pandemic. And models that could…
Epidemiological models have tremendous potential to forecast disease burden and quantify the impact of interventions. Detailed models are increasingly popular, however these models tend to be stochastic and very costly to evaluate.…
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…
This paper presents a probabilistic model for reasoning about the state of a system as it changes over time, both due to exogenous and endogenous influences. Our target domain is a class of medical prediction problems that are neither so…
The main aim to build models capable of simulating the spreading of infectious diseases is to control them. And along this way, the key to find the optimal strategy for disease control is to obtain a large number of simulations of disease…
It is increasingly important to understand the spatial dynamics of epidemics. While there are numerous mathematical models of epidemics, there is a scarcity of physical systems with sufficiently well-controlled parameters to allow…