On the global attractivity of a nonlocal and vector-bias malaria model

This paper investigates global dynamics of an infection age-space structured cholera model. The model describes the vibrio cholerae transmission in human population, where infection-age structure of vibrio cholerae and infectious individuals are incorporated to measure the infectivity during the different stage of disease transmission. The model is described by reaction–diffusion models involving the spatial dispersal of vibrios and the mobility of human populations in the same domain Ω ⊂ ℝ n . We first give the well-posedness of the model by converting the model to a reaction–diffusion model and two Volterra integral equations and obtain two constant equilibria. Our result suggest that the basic reproduction number determines the dichotomy of disease persistence and extinction, which is achieved by studying the local stability of equilibria, disease persistence and global attractivity of equilibria.

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Permanence and Positive Periodic Solutions of a Discrete Delay Competitive System

Discrete Dynamics in Nature and Society ◽

10.1155/2010/381750 ◽

2010 ◽

Vol 2010 ◽

pp. 1-22 ◽

Cited By ~ 2

Author(s):

Wenjie Qin ◽

Zhijun Liu

Keyword(s):

Periodic Solutions ◽

Global Attractivity ◽

Sufficient Conditions ◽

Coincidence Degree ◽

Degree Theory ◽

Discrete Delay ◽

Positive Periodic Solutions ◽

Competitive System ◽

Discrete Function ◽

Species Population

A discrete time non-autonomous two-species competitive system with delays is proposed, which involves the influence of many generations on the density of species population. Sufficient conditions for permanence of the system are given. When the system is periodic, by using the continuous theorem of coincidence degree theory and constructing a suitable Lyapunov discrete function, sufficient conditions which guarantee the existence and global attractivity of positive periodic solutions are obtained. As an application, examples and their numerical simulations are presented to illustrate the feasibility of our main results.

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Plasmodium knowlesi: a relevant, versatile experimental malaria model

Parasitology ◽

10.1017/s0031182016002286 ◽

2016 ◽

Vol 145 (1) ◽

pp. 56-70 ◽

Cited By ~ 8

Author(s):

ERICA M. PASINI ◽

ANNE-MARIE ZEEMAN ◽

ANNEMARIE VOORBERG-VAN DER WEL ◽

CLEMENS H. M. KOCKEN

Keyword(s):

Parasite Species ◽

Vaccine Development ◽

Plasmodium Knowlesi ◽

Host Interactions ◽

Model Studies ◽

Human Red Blood Cells ◽

Malaria Model ◽

Human Primate

SUMMARYThe primate malariaPlasmodium knowlesihas a long-standing history as an experimental malaria model. Studies using this model parasite in combination with its various natural and experimental non-human primate hosts have led to important advances in vaccine development and in our understanding of malaria invasion, immunology and parasite–host interactions. The adaptation to long-termin vitrocontinuous blood stage culture in rhesus monkey,Macaca fascicularisand human red blood cells, as well as the development of various transfection methodologies has resulted in a highly versatile experimental malaria model, further increasing the potential of what was already a very powerful model. The growing evidence thatP. knowlesiis an important human zoonosis in South-East Asia has added relevance to former and future studies of this parasite species.

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Conditions for Almost Global Attractivity of a Synchronous Generator Connected to an Infinite Bus

IEEE Transactions on Automatic Control ◽

10.1109/tac.2017.2671026 ◽

2017 ◽

Vol 62 (10) ◽

pp. 4905-4916 ◽

Cited By ~ 6

Author(s):

Nikita Barabanov ◽

Johannes Schiffer ◽

Romeo Ortega ◽

Denis Efimov

Keyword(s):

Global Attractivity ◽

Synchronous Generator

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Stochasticity and heterogeneity in host–vector models

Journal of The Royal Society Interface ◽

10.1098/rsif.2007.1064 ◽

2007 ◽

Vol 4 (16) ◽

pp. 851-863 ◽

Cited By ~ 57

Author(s):

Alun L Lloyd ◽

Ji Zhang ◽

A.Morgan Root

Keyword(s):

Branching Process ◽

Moment Equations ◽

Demographic Stochasticity ◽

The Face ◽

Process Methodology ◽

The Impact ◽

Malaria Model ◽

Heterogeneous Transmission ◽

Insight Into ◽

Stochastic Extinction

Demographic stochasticity and heterogeneity in transmission of infection can affect the dynamics of host–vector disease systems in important ways. We discuss the use of analytic techniques to assess the impact of demographic stochasticity in both well-mixed and heterogeneous settings. Disease invasion probabilities can be calculated using branching process methodology. We review the use of this theory for host–vector infections and examine its use in the face of heterogeneous transmission. Situations in which there is a marked asymmetry in transmission between host and vector are seen to be of particular interest. For endemic infections, stochasticity leads to variation in prevalence about the endemic level. If these fluctuations are large enough, disease extinction can occur via endemic fade-out. We develop moment equations that quantify the impact of stochasticity, providing insight into the likelihood of stochastic extinction. We frame our discussion in terms of the simple Ross malaria model, but discuss extensions to more realistic host–vector models.

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