A note on epidemic models with infective immigrants and vaccination.
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TL;DR: The roles of immigration and vaccination on disease dynamics are explored in a simple setting that considers the possibility of conferred immunity and conditions for the existence of multiple endemic steady states and a fold bifurcation.
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Abstract: The roles of immigration and vaccination on disease dynamics are explored in a simple setting that considers the possibility of conferred immunity. We focus on SIR and SIS models with a vaccinated class. Conditions for the existence of multiple endemic steady states and a fold bifurcation are discussed.
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Citations
SVIR epidemic models with vaccination strategies.
TL;DR: Mathematical results suggest that vaccination is helpful for disease control by decreasing the basic reproduction number, which is a necessary condition for successful elimination of disease.
286
Optimal Control and Sensitivity Analysis of an Influenza Model with Treatment and Vaccination
TL;DR: It is observed that full treatment effort should be given while increasing vaccination at the onset of the outbreak, and the mostsensitive parameter of the various reproductive numbers apart from the death rate is the inflow rate, while the proportion of new recruits and the vaccine efficacy are the most sensitive parameters for the endemic equilibrium point.
Modelling and analysis of the spread of AIDS epidemic with immigration of HIV infectives
TL;DR: A nonlinear mathematical model of the spread of HIV/AIDS in a population of varying size with immigration of infectives and the endemicity of the disease is found to be higher if pre-AIDS individuals also interact sexually in comparison to the case when they do not take part in sexual interactions.
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Permanence and extinction of a nonautonomous HIV/AIDS epidemic model with distributed time delay
TL;DR: In this paper, the authors considered a non-autonomous stage-structured HIV/AIDS epidemic model with two stages of the period of infection according to the developing progress of infection before AIDS defined in, with varying total population size and distributed time delay to become infectious.
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SIR-SVS epidemic models with continuous and impulsive vaccination strategies.
Jianquan Li,Yali Yang +1 more
TL;DR: Two SIR-SVS epidemic models with vaccination, where it is assumed that the vaccination for the newborns is continuous in the two models, are considered, and two types of vaccination strategies for the susceptible individuals are compared.
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References
Global results for an epidemic model with vaccination that exhibits backward bifurcation
TL;DR: It is shown that a backward bifurcation leading to bistability can occur and under mild parameter constraints, compound matrices are used to show that each orbit limits to an equilibrium.
Backwards bifurcations and catastrophe in simple models of fatal diseases
TL;DR: The ratio S/1 gives the proportion of susceptibles in a population, and hence the probability that a given contact of infectious individual is with a susceptible individual, under the assumption of homogeneous mixing.
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SARS outbreaks in Ontario, Hong Kong and Singapore: the role of diagnosis and isolation as a control mechanism.
Gerardo Chowell,Paul W. Fenimore,M.A. Castillo-Garsow,Carlos Castillo-Chavez,Carlos Castillo-Chavez +4 more
TL;DR: The possibility that 10 or more percent of the world population at risk could eventually be infected with the virus in conjunction with a mortality rate of 3–7% or more, and indications of significant improvement in Toronto support the stringent measures that have been taken to isolate diagnosed cases.
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A core group model for disease transmission
TL;DR: The general conclusion is that partially effective vaccination or education programs may increase the total number of cases while decreasing the relative frequency of cases in the core group, and throws some new light on the role of the reproduction number in connection with elimination attempts.
A Vaccination Model for Transmission Dynamics of Influenza
Murray E. Alexander,Christopher S Bowman,Christopher S Bowman,Seyed M. Moghadas,Randy Summers,Abba B. Gumel,Beni M. Sahai +6 more
TL;DR: Despite the availability of preventive vaccines and public health vaccination programs, influenza inflicts substantial morbidity, mortality, and socio-economic costs and remains a major public heal...
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