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From pathogens and computer viruses to genes and memes, contagion models have found widespread utility across the natural and social sciences. Despite their success and breadth of adoption, the approach and structure of these models remain…
This article reviews and presents various solved and open problems in the development, analysis, and control of epidemic models. We are interested in presenting a relatively concise report for new engineers looking to enter the field of…
This article focuses, in the context of epidemic models, on rare events that may possibly correspond to crisis situations from the perspective of Public Health. In general, no close analytic form for their occurrence probabilities is…
The spreading dynamics of an epidemic and the collective behavioral pattern of the population over which it spreads are deeply intertwined and the latter can critically shape the outcome of the former. Motivated by this, we design a…
Compartmental models are widely adopted to describe and predict the spreading of infectious diseases. The unknown parameters of such models need to be estimated from the data. Furthermore, when some of the model variables are not…
Many widely used models amount to an elaborate means of making up numbers--but once a number has been produced, it tends to be taken seriously and its source (the model) is rarely examined carefully. Many widely used models have little…
A simple, but ``classical``, stochastic model for epidemic spread in a finite, but large, population is studied. The progress of the epidemic can be divided into three different phases that requires different tools to analyse. Initially the…
Metapopulation models are commonly used in ecology, evolution, and epidemiology. These models usually entail homogeneity assumptions within patches and study networks of migration between patches to generate insights into conservation of…
In this work we look at several mathematical models that have been constructed during the present pandemic to address dfferent issues of importance to public health policies about epidemic scenarios and thier causes. We start by briefly…
A stochastic epidemic model is defined in which each individual belongs to a household, a secondary grouping (typically school or workplace) and also the community as a whole. Moreover, infectious contacts take place in these three settings…
Mathematical models of infectious diseases are frequently used as a tool to support public health policy and decisions around implementation of interventions such as school closures. However, most publications on policy-relevant modelling…
Most epidemic models are spatially aggregate and the index which is most used for planning and policy numbers, the r number, typically refers to a single system of interest. Even if r numbers are calculated for each of adjacent areas,…
We summarize recent progress on the theory and applications of structural identifiability of compartmental models. On the applications side, we review identifiability analyses undertaken recently for models arising in epidemiology,…
We discuss the failure of monotonicity properties for even simple compartmental epidemic models, for the case where transmission rates are non-constant. We also identify a special case in which monotonicity holds.
Simulation models are an absolute necessity in the human and social sciences, which can only very exceptionally use experimental science methods to construct their knowledge. Models enable the simulation of social processes by replacing the…
Infectious diseases, either emerging or long-lasting, place numerous people at risk and bring heavy public health burdens worldwide. In the process against infectious diseases, predicting the epidemic risk by modeling the disease…
We describe a new method for evaluating Bayes factors. The key idea is to introduce a hypermodel in which the competing models are components of a mixture distribution. Inference for the mixing probabilities then yields estimates of the…
In recent years the research community has accumulated overwhelming evidence for the emergence of complex and heterogeneous connectivity patterns in a wide range of biological and sociotechnical systems. The complex properties of real-world…
With the rise of computers, simulation models have emerged beside the more traditional statistical and mathematical models as a third pillar for ecological analysis. Broadly speaking, a simulation model is an algorithm, typically…
The paper presents an algorithm for syndromic surveillance of an epidemic outbreak formulated in the context of stochastic nonlinear filtering. The dynamics of the epidemic is modeled using a generalized compartmental epidemiological model…