Global dynamics of an age-structured malaria model with prevention
TLDR
A new age-structured malaria model is formulated, which incorporates the age of prevention period of susceptible people, theAge of latent period of human and the age-of-latent period of female Anopheles mosquitoes, and it is shown that there exists a compact global attractor.Abstract:
In this paper, we formulate a new age-structured malaria model, which incorporates the age of prevention period of susceptible people, the age of latent period of human and the age of latent period of female Anopheles mosquitoes. We show that there exists a compact global attractor and obtain a sufficient condition for uniform persistence of the solution semiflow. We obtain the basic reproduction number R₀ and show that R₀ completely determines the global dynamics of the model, that is, if R₀ 1, there exists a unique endemic equilibrium that attracts all solutions for which malaria transmission occurs. Finally, we perform some numerical simulations to illustrate our theoretical results and give a brief discussion.read more
Citations
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Dynamics of an edge-based SEIR model for sexually transmitted diseases.
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Stability Analysis of an Age-Structured SEIRS Model with Time Delay
Zhe Yin,Yongguang Yu,Zhenzhen Lu +2 more
TL;DR: In this article, the stability of an age-structured susceptible-exposed-infective-recovered-susceptible (SEIRS) model with time delay was investigated.
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Modeling the Effects of Meteorological Factors and Unreported Cases on Seasonal Influenza Outbreaks in Gansu Province, China
TL;DR: A new non-autonomous periodic differential equation model with meteorological factors including unreported cases is proposed and the global asymptotic stability of the disease-free periodic solution is proved, and it is shown that influenza is more likely to spread in low temperature, low humidity and low precipitation environments.
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Analysis of an age-structured tuberculosis model with treatment and relapse
TL;DR: In this paper, a new tuberculosis model consisting of ordinary differential equations and partial differential equations is established, and the basic reproduction number is identified for this model, and show that the $$\mathcal {R}_{0}$$ determines the global dynamics of the model.
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Dynamics of an two-group structured malaria transmission model
TL;DR: In this paper , the authors proposed a two-group malaria model structured by age with the SEIS dynamic in individuals aged below 5 years old, and SEIRS dynamic in those aged above 5 years.
References
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Persistence in infinite-dimensional systems
Jack K. Hale,Paul Waltman +1 more
TL;DR: In this paper, the authors investigated the persistence of a population dynamics model in the setting of a $C^0 $-semigroup which is asymptotically smooth, and provided conditions on the flow on the boundary which, given the presence of a global attractor provided by the assumption of dissipativeness, are necessary and sufficient for persistence.
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Global attractors and steady states for uniformly persistent dynamical systems
Pierre Magal,Xiao-Qiang Zhao +1 more
TL;DR: By appealing to the theory of global attractors on complete metric spaces, this work obtains weaker sufficient conditions for the existence of interior global attractor for uniformly persistent dynamical systems, and hence generalize the earlier results on coexistence steady states.
Book
Dynamical Systems and Population Persistence
Hal L. Smith,Horst R. Thieme +1 more
TL;DR: The mathematical theory of persistence answers questions such as which species, in a mathematical model of interacting species, will survive over the long term as mentioned in this paper, and applies to infinite-dimensional as well as to finite-dimensional dynamical systems.