Showing papers by "Robert J. Smith published in 2015"
TL;DR: It is proved that the avian-only model achieves global stability and by choosing an appropriate quarantine threshold level I c in the SIIR model, this model converges to an equilibrium in the region below I c or a sliding equilibrium, suggesting the outbreak can be controlled.
Abstract: The growing number of reported avian influenza cases has prompted awareness of the effectiveness of pharmaceutical or/and non-pharmaceutical interventions that aim to suppress the transmission rate We propose two Filippov models with threshold policy: the avian-only model with culling of infected birds and the SIIR (Susceptible–Infected–Infected–Recovered) model with quarantine The dynamical systems of these two models are governed by nonlinear ordinary differential equations with discontinuous right-hand sides The solutions of these two models will converge to either one of the two endemic equilibria or the sliding equilibrium on the discontinuous surface We prove that the avian-only model achieves global stability Moreover, by choosing an appropriate quarantine threshold level I c in the SIIR model, this model converges to an equilibrium in the region below I c or a sliding equilibrium, suggesting the outbreak can be controlled Therefore a well-defined threshold policy is important for us to combat the influenza outbreak efficiently
28 citations
TL;DR: In this paper, a mathematical model accounting for the disease dynamics in connected regions, incorporating seasonality, environmental reservoirs and independent periodic pulse vaccination schedules in each region, is proposed and proved to be a global threshold for persistence of the disease.
Abstract: 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, \(R_e\), 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 \(R_e\) 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 \(R_e\) when pulse vaccination is present.
22 citations
01 Jan 2015
TL;DR: In this article, an exposition on matrix solutions, their properties and Floquet's theorem for periodic linear systems is provided, including applications to stability, where applicable, comparison is made to the analoguous results from impulsive dierential equations.
Abstract: Analogues of the classical existence and uniqueness of solutions are proven for impulse extension equations. An exposition on matrix solutions, their properties and Flo- quet's theorem for periodic linear systems is provided, including applications to stability. Where applicable, comparison is made to the analoguous results from impulsive dierential equations. equation, impulse extension, predictable set, matrix solution, fundamental matrix, periodic solution, Floquet's theorem. AMS (MOS) subject classication: 34A36, 34A37.
8 citations
TL;DR: Different mathematical models and methods that have been used to estimate risk of BSE are summarized, and how such risk projection models have informed risk assessment and management of Bse is discussed.
Abstract: When the bovine spongiform encephalopathy (BSE) epidemic first emerged in the United Kingdom in the mid 1980s, the etiology of animal prion diseases was largely unknown. Risk management efforts to control the disease were also subject to uncertainties regarding the extent of BSE infections and future course of the epidemic. As understanding of BSE increased, mathematical models were developed to estimate risk of BSE infection and to predict reductions in risk in response to BSE control measures. Risk models of BSE-transmission dynamics determined disease persistence in cattle herds and relative infectivity of cattle prior to onset of clinical disease. These BSE models helped in understanding key epidemiological features of BSE transmission and dynamics, such as incubation period distribution and age-dependent infection susceptibility to infection with the BSE agent. This review summarizes different mathematical models and methods that have been used to estimate risk of BSE, and discusses how such risk projection models have informed risk assessment and management of BSE. This review also provides some general insights on how mathematical models of the type discussed here may be used to estimate risks of emerging zoonotic diseases when biological data on transmission of the etiological agent are limited.
7 citations
TL;DR: The model suggests the grade of vaccination and the number of doses do not make a significant difference to the outcome of the public vaccination program and the main focus of the program should be on obtaining a large enough coverage rate for children and/or adults in order to achieve the desired outcome.
Abstract: Human papillomavirus (HPV) infection is the most common sexually transmitted infection, which is linked to several cancers and genital warts. Depending on the Canadian province, the quadrivalent vaccine is given to girls in grades 4 through 10 with either a two- or three-dose schedule. We use a mathematical model to address the following research questions: (1) Does the grade at which the girls are vaccinated significantly affect the outcome of the program? (2) What coverage rate must the provinces reach in order to reduce the impact of HPV on the Canadian population? (3) What are the implications of vaccinating with two versus three doses? The model suggests the grade of vaccination and the number of doses do not make a significant difference to the outcome of the public vaccination program. The most significant factor is the coverage rate of children and adults. We recommend that provinces vaccinate as early as possible to avoid vaccine failure due to previous infection. We also recommend that the main focus of the program should be on obtaining a large enough coverage rate for children and/or adults in order to achieve the desired outcome with either two or three doses of the vaccine.
4 citations
TL;DR: It is shown that education, if it is properly harnessed, can be a force strong enough to overcome the effects of antiretroviral drug resistance; however, in the absence of education, “test and treat” is likely to make the epidemic worse.
Abstract: Recent mathematical modelling has advocated for rapid “test-and-treat” programs for HIV in the developing world, where HIV-positive individuals are identified and immediately begin a course of antiretroviral treatment, regardless of the length of time they have been infected. However, the foundations of this modelling ignored the effects of drug resistance on the epidemic. It also disregarded the heterogeneity of behaviour changes that may occur, as a result of education that some individuals may receive upon testing and treatment. We formulate an HIV/AIDS model to theoretically investigate how testing, educating HIV-positive cases, treatment, and drug resistance affect the HIV epidemic. We consider a variety of circumstances: both when education is included and not included, when testing and treatment are linked or are separate, when education is only partly effective, and when treatment leads to drug resistance. We show that education, if it is properly harnessed, can be a force strong enough to overcome the effects of antiretroviral drug resistance; however, in the absence of education, “test and treat” is likely to make the epidemic worse.
3 citations