相关论文: Edge-based compartmental modeling for epidemic spr…
We consider the spread of infectious diseases through a Mean Field Game version of a SIR compartmental model with social structure, in which individuals are grouped by their age class and interact together in different settings. In our game…
Deterministic compartmental models are predominantly used in the modeling of infectious diseases, though stochastic models are considered more realistic, yet are complicated to estimate due to missing data. In this paper we present a novel…
Many models of epidemic spread have a common qualitative structure. The numbers of infected individuals during the initial stages of an epidemic can be well approximated by a branching process, after which the proportion of individuals that…
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.…
In Part 1, we introduced a stochastic model of an infectious disease, based on the BDI (birth and death with immigration) process. We showed that random processes defined by this model can capture the essence of the stochastic, often…
Network-based models of epidemic spread have become increasingly popular in recent decades. Despite a rich foundation of such models, few low-dimensional systems for modeling SIS-type diseases have been proposed that manage to capture the…
The impact of spatial structure on the spread of an epidemic is an important issue in the propagation of infectious diseases. Recent studies, both deterministic and stochastic, have made it possible to understand the importance of the…
Pandemics can cause immense disruption and damage to communities and societies. Thus far, modeling of pandemics has focused on either large-scale difference equation models like the SIR and the SEIR models, or detailed micro-level…
Epidemiological models describe the spread of an infectious disease within a population. They capture microscopic details on how the disease is passed on among individuals in various different ways, while making predictions about the state…
We analyze four models of epidemic spreading using a stochastic approach in which the primary stochastic variables are the numbers of individuals in each class. The stochastic approach is described by a master equation and the transition…
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,…
A Markovian SIR (Susceptible-Infectious-Recovered) model is considered for the spread of an epidemic on a configuration model network, in which susceptible individuals may take preventive measures by dropping edges to infectious neighbours.…
In this research, we develop a framework to analyze the interaction between the economy and the Covid-19 pandemic using an extension of SIR epidemic model. At the outset, we assume there are two health related investments including general…
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…
As the global HIV pandemic enters its fourth decade, increasing numbers of surveillance sites have been established which allows countries to look into the epidemics at a finer scale, e.g. at sub-national level. However, the epidemic models…
We introduce a numerical method to solve epidemic models on the underlying topology of complex networks. The approach exploits the mean-field like rate equations describing the system and allows to work with very large system sizes, where…
This brief note highlights a largely overlooked similarity between the SIR ordinary differential equations used for epidemics on the configuration model of a Poisson network and the classical mass-action SIR equations introduced nearly a…
Networks of contacts capable of spreading infectious diseases are often observed to be highly heterogeneous, with the majority of individuals having fewer contacts than the mean, and a significant minority having relatively very many…
Infectious disease superspreading caused by heterogeneity in contact behavior has been observed to be an important determinant of epidemic dynamics and size in both empirical and theoretical settings. However, it has also been observed that…
This is work in progress. We make it accessible hoping that people might find the idea useful. We propose a discrete, recursive 5-compartment model for the spread of epidemics, which we call {\em SEPIR-model}. Under mild assumptions which…