239 research outputs found
On the net reproduction rate of continuous structured populations with distributed states at birth
We consider a nonlinear structured population model with a distributed
recruitment term. The question of the existence of non-trivial steady states
can be treated (at least!) in three different ways. One approach is to study
spectral properties of a parametrized family of unbounded operators. The
alternative approach, on which we focus here, is based on the reformulation of
the problem as an integral equation. In this context we introduce a density
dependent net reproduction rate and discuss its relationship to a biologically
meaningful quantity. Finally, we briefly discuss a third approach, which is
based on the finite rank approximation of the recruitment operator.Comment: To appear in Computers and Mathematics with Application
Numerical analysis of generalised max-plus eigenvalue problems
AbstractThis paper is concerned with the deterministic discrete-time infinite horizon optimisation problem on a compact metric space with an average cost criterion involving two functions K (the “cost”) and T (the “time”). Firstly, we collect the different characterisations of the value λ in terms of generalised max-plus eigenvalue problem and in terms of linear programming. Secondly, we prove an error bound on λ when the space is discretised
Stage‐structured population systems with temporally periodic delay
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/115917/1/mma3424_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/115917/2/mma3424.pd
A study on vaccination models for a seasonal epidemic process
In this paper seasonal epidemiological processes are considered and a strategy of periodic vaccination is proposed. The invariant formulations associated with an N-periodic system and the reproduction numbers associated with them are considered. A collection of measures to study the stability of the system is introduced. Moreover, the collection of s-basic reproduction number at time j help us to establish conditions on the periodic vaccination rates in the vaccination program. Finally, an SIR model is showed and a comparison between the results obtained using constant or periodic vaccination program is analyzed. (C) 2014 Elsevier Inc. All rights reserved.The authors wish to express their thanks to the reviewers for helpful comments and suggestions. This paper is supported by Grant MTM2010-18228.Cantó Colomina, B.; Coll, C.; Sánchez, E. (2014). A study on vaccination models for a seasonal epidemic process. Applied Mathematics and Computation. 243:152-160. https://doi.org/10.1016/j.amc.2014.05.104S15216024
Evaluating the Cost-Effectiveness of Pre-Exposure Prophylaxis (PrEP) and Its Impact on HIV-1 Transmission in South Africa
The original publication is available at http:/www.plosone.orgBackground: Mathematical modelers have given little attention to the question of how pre-exposure prophylaxis (PrEP) may impact on a generalized national HIV epidemic and its cost-effectiveness, in the context of control strategies such as condom use promotion and expanding ART programs. Methodology/Principal Findings: We use an age- and gender-structured model of the generalized HIV epidemic in South Africa to investigate the potential impact of PrEP in averting new infections. The model utilizes age-structured mortality, fertility, partnership and condom use data to model the spread of HIV and the shift of peak prevalence to older age groups. The model shows that universal PrEP coverage would have to be impractically high to have a significant effect on incidence reduction while ART coverage expands. PrEP targeted to 15-35-year-old women would avert 10%-25% (resp. 13%-28%) of infections in this group and 5%-12% (resp. 7%-16%) of all infections in the period 2014-2025 if baseline incidence is 0.5% per year at 2025 (resp. 0.8% per year at 2025). The cost would be 20,000 per infection averted, depending on the level of ART coverage and baseline incidence. An optimistic scenario of 30%-60% PrEP coverage, efficacy of at least 90%, no behavior change among PrEP users and ART coverage less than three times its 2010 levels is required to achieve this result. Targeting PrEP to 25-35-year-old women (at highest risk of infection) improves impact and cost-effectiveness marginally. Relatively low levels of condom substitution (e.g., 30%) do not nullify the efficacy of PrEP, but reduces cost-effectiveness by 35%-40%. Conclusions/Significance: PrEP can avert as many as 30% of new infections in targeted age groups of women at highest risk of infection. The cost-effectiveness of PrEP relative to ART decreases rapidly as ART coverage increases beyond three times its coverage in 2010, after which the ART program would provide coverage to more than 65% of HIV+ individuals. To have a high relative cost-effective impact on reducing infections in generalized epidemics, PrEP must utilize a window of opportunity until ART has been scaled up beyond this level. © 2010 Pretorius et al.Publishers' Versio
A Metapopulation Model for Chikungunya Including Populations Mobility on a Large-Scale Network
In this work we study the influence of populations mobility on the spread of
a vector-borne disease. We focus on the chikungunya epidemic event that
occurred in 2005-2006 on the R\'eunion Island, Indian Ocean, France, and
validate our models with real epidemic data from the event. We propose a
metapopulation model to represent both a high-resolution patch model of the
island with realistic population densities and also mobility models for humans
(based on real-motion data) and mosquitoes. In this metapopulation network, two
models are coupled: one for the dynamics of the mosquito population and one for
the transmission of the disease. A high-resolution numerical model is created
out from real geographical, demographical and mobility data. The Island is
modeled with an 18 000-nodes metapopulation network. Numerical results show the
impact of the geographical environment and populations' mobility on the spread
of the disease. The model is finally validated against real epidemic data from
the R\'eunion event.Comment: Accepted in Journal of Theoretical biolog
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
Basic Reproduction Number of Chikungunya Virus Transmitted by Aedes Mosquitoes
We estimated the weighted mean basic reproduction number (R0) of chikungunya virus based on outbreak size. R0 was 3.4 (95% CI 2.4–4.2) and varied for 2 primary chi- kungunya mosquito vectors: 4.1 (95% CI 1.5–6.6) for Ae- des aegypti and 2.8 (95% CI 1.8–3.8) for Ae. albopictu
New results on the existences of solutions of the Dirichlet problem with respect to the Schrödinger-prey operator and their applications
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