704 research outputs found
From regional pulse vaccination to global disease eradication: insights from a mathematical model of Poliomyelitis
Mass-vaccination campaigns are an important strategy in the global fight
against poliomyelitis and measles. The large-scale logistics required for these
mass immunisation campaigns magnifies the need for research into the
effectiveness and optimal deployment of pulse vaccination. In order to better
understand this control strategy, we propose a mathematical model accounting
for the disease dynamics in connected regions, incorporating seasonality,
environmental reservoirs and independent periodic pulse vaccination schedules
in each region. The effective reproduction number, , is defined and proved
to be a global threshold for persistence of the disease. Analytical and
numerical calculations show the importance of synchronising the pulse
vaccinations in connected regions and the timing of the pulses with respect to
the pathogen circulation seasonality. Our results indicate that it may be
crucial for mass-vaccination programs, such as national immunisation days, to
be synchronised across different regions. In addition, simulations show that a
migration imbalance can increase and alter how pulse vaccination should
be optimally distributed among the patches, similar to results found with
constant-rate vaccination. Furthermore, contrary to the case of constant-rate
vaccination, the fraction of environmental transmission affects the value of
when pulse vaccination is present.Comment: Added section 6.1, made other revisions, changed titl
Global stability of vaccine-age/staged-structured epidemic models with nonlinear incidence
We consider two classes of infinitely dimensional epidemic models with nonlinear incidence, where one assumes that the rate of a vaccinated individual losing immunity depends on the vaccine-age and another assumes that, before the vaccine begins to wane, there is a period during which the vaccinated individuals have complete immunity against the infection. The first model is given by a coupled ordinary-hyperbolic differential system and the second class is described by a delay differential system. We calculate their respective basic reproduction numbers, and show they characterize the global dynamics by constructing the appropriate Lyapunov functionals
Nonlinear pulse vaccination in an SIR epidemic model with resource limitation
Mathematical models can assist in the design and understanding of vaccination strategies when resources are limited. Here we propose and analyse an SIR epidemic modelwith a nonlinear pulse vaccination to examine how a limited vaccine resource affects the transmission and control of infectious diseases, in particular emerging infectious diseases. The threshold condition for the stability of the disease free steady state is given. Latin Hypercube Sampling/Partial Rank Correlation Coefficient uncertainty and sensitivity analysis techniques were employed to determine the key factors which are most significantly related to the threshold value. Comparing this threshold value with that without resource limitation, our results indicate that if resources become limited pulse
vaccination should be carried out more frequently than when sufficient resources are available to eradicate an infectious disease. Once the threshold value exceeds a critical level, both susceptible and infected populations can oscillate periodically. Furthermore, when the pulse vaccination period is chosen as a bifurcation parameter, the SIR model with nonlinear pulse vaccination reveals
complex dynamics including period doubling, chaotic solutions, and coexistence of multiple attractors. The implications of our findings with respect to disease control are discussed
Analysis of an SIR Epidemic Model with Pulse Vaccination and Distributed Time Delay
Pulse vaccination, the repeated application of
vaccine over a defined age range, is gaining prominence as an
effective strategy for the elimination of infectious diseases. An
SIR epidemic model with pulse vaccination and distributed time delay is proposed in this paper. Using the discrete dynamical
system determined by the stroboscopic map, we obtain the exact
infection-free periodic solution of the impulsive epidemic system
and prove that the infection-free periodic solution is globally attractive if the vaccination rate is larger enough. Moreover, we
show that the disease is uniformly persistent if the vaccination
rate is less than some critical value. The permanence of the model is
investigated analytically. Our results indicate that a large pulse
vaccination rate is sufficient for the eradication of the disease
Mitigating Epidemics through Mobile Micro-measures
Epidemics of infectious diseases are among the largest threats to the quality
of life and the economic and social well-being of developing countries. The
arsenal of measures against such epidemics is well-established, but costly and
insufficient to mitigate their impact. In this paper, we argue that mobile
technology adds a powerful weapon to this arsenal, because (a) mobile devices
endow us with the unprecedented ability to measure and model the detailed
behavioral patterns of the affected population, and (b) they enable the
delivery of personalized behavioral recommendations to individuals in real
time. We combine these two ideas and propose several strategies to generate
such recommendations from mobility patterns. The goal of each strategy is a
large reduction in infections, with a small impact on the normal course of
daily life. We evaluate these strategies over the Orange D4D dataset and show
the benefit of mobile micro-measures, even if only a fraction of the population
participates. These preliminary results demonstrate the potential of mobile
technology to complement other measures like vaccination and quarantines
against disease epidemics.Comment: Presented at NetMob 2013, Bosto
Global attractivity and permanence of a SVEIR epidemic model with pulse vaccination and time delay
AbstractIn this study, we propose a new SVEIR epidemic disease model with time delay, and analyze the dynamic behavior of the model under pulse vaccination. Pulse vaccination is an effective strategy for the elimination of infectious disease. Using the discrete dynamical system determined by the stroboscopic map, we obtain an ‘infection-free’ periodic solution. We also show that the ‘infection-free’ periodic solution is globally attractive when some parameters of the model under appropriate conditions. The permanence of the model is investigated analytically. Our results indicate that a large vaccination rate or a short pulse of vaccination or a long latent period is a sufficient condition for the extinction of the disease
Stability analysis of drinking epidemic models and investigation of optimal treatment strategy
In this research we investigate a class of drinking epidemic models, namely the SPARS type models. The basic reproduction number is derived, and the system dynamical behaviours are investigated for both drinking free equilibrium and drinking persistent equilibrium. The purpose is to determine the long term optimal treatment method and the optimal short period vaccination strategy for controlling the population of the periodic drinkers and alcoholics
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