351 research outputs found
Dynamic models for the analysis of epidemic spreads Modelli dinamici per l'analisi di diffusioni epidemiche
Quest'elaborato studia e analizza il modello SIR o di Kermack-McKendrick sulle diffusioni epidemiche svillupato nel 1927. In seguito vengono prese in considerazione diverse sue generalizzazioni per adattarlo a situazioni più complesse. Infine applichiamo il modello a dei reali focolai epidemici e ne valutiamo le simulazione tramite Matla
Mathematical models for the analysis of hepatitis B and AIDS epidemics
Continuous simulation mathematical models are proposed for two different epidemic situations: Hepatitis B in a cohort of newborns followed for life, and one of the danger groups in the current AIDS epidemic. The paper describes the rational behind the systems of differential equations used to model both situations, and the way to test alternative policies, such as vaccination, preventive measures, or the effects
of new drugs on AIDS
Coupled Contagion Dynamics of Fear and Disease: Mathematical and Computational Explorations
Background: In classical mathematical epidemiology, individuals do not adapt their contact behavior during epidemics. They do not endogenously engage, for example, in social distancing based on fear. Yet, adaptive behavior is welldocumented in true epidemics. We explore the effect of including such behavior in models of epidemic dynamics. Methodology/Principal Findings: Using both nonlinear dynamical systems and agent-based computation, we model two interacting contagion processes: one of disease and one of fear of the disease. Individuals can ‘‘contract’ ’ fear through contact with individuals who are infected with the disease (the sick), infected with fear only (the scared), and infected with both fear and disease (the sick and scared). Scared individuals–whether sick or not–may remove themselves from circulation with some probability, which affects the contact dynamic, and thus the disease epidemic proper. If we allow individuals to recover from fear and return to circulation, the coupled dynamics become quite rich, and can include multiple waves of infection. We also study flight as a behavioral response. Conclusions/Significance: In a spatially extended setting, even relatively small levels of fear-inspired flight can have a dramatic impact on spatio-temporal epidemic dynamics. Self-isolation and spatial flight are only two of many possible actions that fear-infected individuals may take. Our main point is that behavioral adaptation of some sort must b
Invited review: Epidemics on social networks
Since its first formulations almost a century ago, mathematical models for
disease spreading contributed to understand, evaluate and control the epidemic
processes.They promoted a dramatic change in how epidemiologists thought of the
propagation of infectious diseases.In the last decade, when the traditional
epidemiological models seemed to be exhausted, new types of models were
developed.These new models incorporated concepts from graph theory to describe
and model the underlying social structure.Many of these works merely produced a
more detailed extension of the previous results, but some others triggered a
completely new paradigm in the mathematical study of epidemic processes. In
this review, we will introduce the basic concepts of epidemiology, epidemic
modeling and networks, to finally provide a brief description of the most
relevant results in the field.Comment: 17 pages, 13 figure
The interplay between models and public health policies: Regional control for a class of spatially structured epidemics (think globally, act locally)
A review is presented here of the research carried out, by a group including the authors, on the mathematical analysis of epidemic systems. Particular attention is paid to recent analysis of optimal control problems related to spatially structured epidemics driven by environmental pollution. A relevant problem, related to the possible eradication of the epidemic, is the so called zero stabilization. In a series of papers, necessary conditions, and sufficient conditions of stabilizability have been obtained. It has been proved that it is possible to diminish exponentially the epidemic process, in the whole habitat, just by reducing the concentration of the pollutant in a nonempty and sufficiently large subset of the spatial domain. The stabilizability with a feedback control of harvesting type is related to the magnitude of the principal eigenvalue of a certain operator. The problem of finding the optimal position (by translation) of the support of the feedback stabilizing control is faced, in order to minimize both the infected population and the pollutant at a certain finite time
Quantifying the transmission potential of pandemic influenza
This article reviews quantitative methods to estimate the basic reproduction
number of pandemic influenza, a key threshold quantity to help determine the
intensity of interventions required to control the disease. Although it is
difficult to assess the transmission potential of a probable future pandemic,
historical epidemiologic data is readily available from previous pandemics, and
as a reference quantity for future pandemic planning, mathematical and
statistical analyses of historical data are crucial. In particular, because
many historical records tend to document only the temporal distribution of
cases or deaths (i.e. epidemic curve), our review focuses on methods to
maximize the utility of time-evolution data and to clarify the detailed
mechanisms of the spread of influenza. First, we highlight structured epidemic
models and their parameter estimation method which can quantify the detailed
disease dynamics including those we cannot observe directly.
Duration-structured epidemic systems are subsequently presented, offering firm
understanding of the definition of the basic and effective reproduction
numbers. When the initial growth phase of an epidemic is investigated, the
distribution of the generation time is key statistical information to
appropriately estimate the transmission potential using the intrinsic growth
rate. Applications of stochastic processes are also highlighted to estimate the
transmission potential using the similar data. Critically important
characteristics of influenza data are subsequently summarized, followed by our
conclusions to suggest potential future methodological improvements.Comment: 79 pages (revised version), 3 figures; added 1 table and minor
revisions were made in the main text; to appear in Physics of Life Reviews;
Gerardo's website (http://www.public.asu.edu/~gchowel/), Hiroshi's website
(http://plaza.umin.ac.jp/~infepi/hnishiura.htm
Modelling of COVID-19 Using Fractional Differential Equations
In this work, we have described the mathematical modeling of COVID-19 transmission using fractional differential equations. The mathematical modeling of infectious disease goes back to the 1760s when the famous mathematician Daniel Bernoulli used an elementary version of compartmental modeling to find the effectiveness of deliberate smallpox inoculation on life expectancy. We have used the well-known SIR (Susceptible, Infected and Recovered) model of Kermack & McKendrick to extend the analysis further by including exposure, quarantining, insusceptibility and deaths in a SEIQRDP model. Further, we have generalized this model by using the solutions of Fractional Differential Equations to test the accuracy and validity of the mathematical modeling techniques against Canadian COVID-19 trends and spread of real-world disease. Our work also emphasizes the importance of Personal Protection Equipment (PPE) and impact of social distancing on controlling the spread of COVID-19
Optimal Vaccination Policy to Prevent Endemicity: A Stochastic Model
We examine here the effects of recurrent vaccination and waning immunity on
the establishment of an endemic equilibrium in a population. An
individual-based model that incorporates memory effects for transmission rate
during infection and subsequent immunity is introduced, considering
stochasticity at the individual level. By letting the population size going to
infinity, we derive a set of equations describing the large scale behavior of
the epidemic. The analysis of the model's equilibria reveals a criterion for
the existence of an endemic equilibrium, which depends on the rate of immunity
loss and the distribution of time between booster doses. The outcome of a
vaccination policy in this context is influenced by the efficiency of the
vaccine in blocking transmissions and the distribution pattern of booster doses
within the population. Strategies with evenly spaced booster shots at the
individual level prove to be more effective in preventing disease spread
compared to irregularly spaced boosters, as longer intervals without
vaccination increase susceptibility and facilitate more efficient disease
transmission. We provide an expression for the critical fraction of the
population required to adhere to the vaccination policy in order to eradicate
the disease, that resembles a well-known threshold for preventing an outbreak
with an imperfect vaccine. We also investigate the consequences of unequal
vaccine access in a population and prove that, under reasonable assumptions,
fair vaccine allocation is the optimal strategy to prevent endemicity.Comment: 49 pages, 7 figure
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