Disease persistence in epidemiological models: The interplay between vaccination and migration

Burton, Jackson; Billings, Lora; Cummings, Derek A. T.; Schwartz, Ira B.

doi:10.1016/j.mbs.2012.05.003

Cited by 21 publications

(23 citation statements)

References 15 publications

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“…The spatial dynamics of multi-species epidemic models is widely discussed in the literature (see [15,16,17,18,19,20,21,22,23] and the reference therein). For a purely deterministic model the account of different dynamics of host and guest species on the epidemic speed was studied in [7].…”

Section: Discussionmentioning

confidence: 99%

Random migration processes between two stochastic epidemic centers

Sazonov

Kelbert

Gravenor

2016

Mathematical Biosciences

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We consider the epidemic dynamics in stochastic interacting population centers coupled by random migration. Both the epidemic and the migration processes are modeled by Markov chains. We derive explicit formulae for the probability distribution of the migration process, and explore the dependence of outbreak patterns on initial parameters, population sizes and coupling parameters, using analytical and numerical methods. We show the importance of considering the movement of resident and visitor individuals separately. The mean field approximation for a general migration process is derived and an approximate method that allows the computation of statistical moments for networks with highly populated centers is proposed and tested numerically.

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Section: Discussionmentioning

confidence: 99%

Random migration processes between two stochastic epidemic centers

Sazonov

Kelbert

Gravenor

2016

Mathematical Biosciences

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“…Hence Φ(τ, ǫ) is continuous with respect to ǫ. So, for ǫ sufficiently small, r(ǫ) = ρ(Φ(τ, ǫ)) < 1 since r(0) = r < 1 by (13). The matrix…”

Section: Threshold Dynamicsmentioning

confidence: 97%

From regional pulse vaccination to global disease eradication: insights from a mathematical model of poliomyelitis

2014

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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, Re, 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 Re 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 Re when pulse vaccination is present.against polio and measles is mass immunisation, which may be regarded as a pulse vaccination [9]. The complex logistics required for these mass-immunisation campaigns magnifies the need for research into the effectiveness and optimal deployment of pulse vaccination [43].Pulse vaccination has been investigated in several mathematical models, often in disease models with seasonal transmission. Many diseases show seasonal patterns in circulation; thus inclusion of seasonality may be crucial. Agur et al. (1993) argued for pulse vaccination using a model of seasonal measles transmission, conjecturing that the pulses may antagonise the periodic disease dynamics and achieve control at a reduced cost of vaccination [1]. Shulgin et al. (1998) investigated the local stability of the disease-free periodic solution in a seasonally forced population model with three groups: susceptible (S), infected (I) and recovered (R).They considered pulse vaccination and explicitly found the threshold pulsing period [31]. Recently, Onyango and Müller considered optimal periodic vaccination strategies in the seasonally forced SIR model and found that a well-timed pulse is optimal, but its effectiveness is often close to that of constant-rate vaccination [28].In addition to seasonality, spatial structure has been recognised as an important factor for disease dynamics and control [38]. Heterogeneity in the population movement, along with the patchy distribution of populations, suggests the use of metapopulation models describing disease transmission in patches or spatially structured populations or regions. Mobility can be incorporated and tracked in these models in vari...

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“…69 The spread of Hansen's disease (HD) 70 and the concern of Herd Immunity 71 are examples of how undocumented immigration impacts public health in the United States. 72 Undocumented immigration has the potential to put the United States at risk for outbreaks of infectious disease, while simultaneously masking the individual source of the threat. 73 This makes mitigation of the potential danger that much more difficult to achieve.…”

Section: Undocumented Immigration and Public Healthmentioning

confidence: 99%

The Potential Impact of Border Security Upon Prevalence of Infectious Disease

Dallas

Harris

Dallas

2018

Disaster med. public health prep.

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In the U.S., migration has been documented to affect the prevalence of infectious disease. As a mitigation entity, border security has been recorded by numerous scholarly works as being essential to the support of the health of the U.S. population. Consequently, the lack of current health care monitoring of the permeable U.S. border places the U.S. population at risk in the broad sectors of infectious disease and interpersonal violence. Visualizing border security in the context of public health mitigation has significant potential to protect migrant health as well as that of all populations on both sides of the border. Examples of how commonly this philosophy is held can be found in the expansive use of security-focused terms regarding public health. Using tools such as GIS to screen for disease in people before their entrance into a nation would be more efficient and ethical than treating patients once they have entered a population and increased the impact on the healthcare system. (Disaster Med Public Health Preparedness. 2018;12:554-562).

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Disease persistence in epidemiological models: The interplay between vaccination and migration

Cited by 21 publications

References 15 publications

Random migration processes between two stochastic epidemic centers

Random migration processes between two stochastic epidemic centers

From regional pulse vaccination to global disease eradication: insights from a mathematical model of poliomyelitis

The Potential Impact of Border Security Upon Prevalence of Infectious Disease

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