Threshold dynamics of a vector-borne disease model with spatial structure and vector-bias

Wang, Jinliang; Chen, Yuming

doi:10.1016/j.aml.2019.106052

Cited by 21 publications

(13 citation statements)

References 16 publications

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“…Specifically, we re-establish the GAS of DFSS in a simple and direct manner and furthermore, resolve the GAS of ESS by rigorous mathematical theory. Here, the method adopted is Lyapunov's direct functional, which had been used widely to derive the global stability in various of epidemic models, such as ordinary differential models, 2,3 delay epidemic models, 4,5 age-structured models, [6][7][8][9][10] reaction-diffusion models, 11,12 and nonlocal diffusion models, 13,14 and so on. The key skill for constructing Lyapunov functionals is to select some novel appropriate kernel functions.…”

Section: Introductionmentioning

confidence: 99%

On the global stability of an age‐structured tuberculosis transmission model with relapse

Liu

Zhang

et al. 2022

Math Methods in App Sciences

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where the global asymptotic stability (GAS) of the endemic steady state (ESS) was unresolved when ℜ 0 > 1. We recompute the existence of ESS in detail, re-establish the GAS of the disease-free steady state (DFSS) in a simple and direct manner, and, furthermore, resolve the GAS of ESS, which was left as an open problem in the above paper. We adopt the method of Lyapunov functional with a key skill of selecting some novel appropriate kernel functions.

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Section: Introductionmentioning

confidence: 99%

On the global stability of an age‐structured tuberculosis transmission model with relapse

Liu

Zhang

et al. 2022

Math Methods in App Sciences

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“…The first models of this category were, to our knowledge, proposed fifteen years ago by Funka et al (2005) and Wang and Wang (2007). More recent treatments are described in articles by Bocharov et al (2018a), Bocharov et al (2019), Huang et al (2019), Tang et al (2019), Yang and Wang (2019), , , Segredo-Otero and Sanjuan (2020), Tadmon and Foko (2020), Wang and Chen (2020) and . The focus in all these studies was primarily on analyzing the propagation of an infection front [reviewed in Sec.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the initiation of viral infection under flow conditions with applications to transmission in feed

Zhdanov

Jackman

2020

Biosystems

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While kinetic models are widely used to describe viral infection at various levels, most of them are focused on temporal aspects and understanding of corresponding spatio-temporal aspects remains limited. In this work, our attention is focused on the initial stage of infection of immobile cells by virus particles (''virions'') under flow conditions with diffusion. A practical example of this scenario occurs when humans or animals consume food from virion-containing sources. Mathematically, such situations can be described by using a model constructed in analogy with those employed in chemical engineering for analysis of the function of a plug-flow reactor with dispersion. As in the temporal case, the corresponding spatio-temporal model predicts either the transition to a steady state or exponential growth of the populations of virions and infected cells. The spatial distributions of these species are similar in both of these regimes. In particular, the maximums of the populations are shifted to the upper boundary of the infected region. The results illustrating these conclusions were obtained analytically and by employing numerical calculations without and with the dependence of the kinetic parameters on the coordinate. The model proposed has also been used in order to illustrate the effect of antiviral feed additives on feedborne infection towards curbing disease transmission.

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“…It was shown that mosquito encounters with susceptible hosts are as likely as mosquito encounters with infected hosts, but that bites occur in infected hosts with a higher probability. Thereafter, numerous studies on vector-bias were conducted, with a focus on the periodicity of mosquito abundance [28], time-delay [29], fractional-order [30], spatial structure [31], and real-world application [32]. It can be seen that the aforementioned studies dealing with the modelling of vector-bias focused on the impacts of the long-term behavioural dynamics.…”

Section: Introductionmentioning

confidence: 99%

Impact of Behavioural Changes in Mosquito Feeding on Malaria Invasion: A Model-Based Approach

Kim

et al. 2020

Preprint

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Background: Malaria hosts are known to manipulate the feeding behaviour of mosquitoes to protect them from external threats and control. In particular, the phenomenon in which a mosquito's feeding target is biased toward an infectious host is called a vector-bias, and it can be a threat to malaria eradication if not considered. Aim of the study is to understand the problems that may arise when vector-bias is not considered in early invasion scenarios.Methods: Stochastic formulations of malaria transmission, including the vector-bias effect, ware constructed. Invasive dynamics were investigated using an individual-based continuous time Markov chain model and the offspring distributions of secondary infections. In addition, the extinction probability was derived using the negative binomial count model. Results: Invasions will occur quickly, and once the disease spreads, extinction will become difficult compared to when the vector-bias effect is not considered. In a highly heterogeneous environment, vector-bias has rare effect on decreasing the extinction probability. Conclusion: The early detection of a malaria invasion and the early control beginning are more important due to vector-bias for the malaria eradication in early invasion scenarios. In addition, some possible mosquito-biased behaviours were discussed in terms of adaptive dynamics.

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Threshold dynamics of a vector-borne disease model with spatial structure and vector-bias

Cited by 21 publications

References 16 publications

On the global stability of an age‐structured tuberculosis transmission model with relapse

On the global stability of an age‐structured tuberculosis transmission model with relapse

Analysis of the initiation of viral infection under flow conditions with applications to transmission in feed

Impact of Behavioural Changes in Mosquito Feeding on Malaria Invasion: A Model-Based Approach

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