Global Dynamics of a New Huanglongbing Transmission Model with Quarantine Measures

<p style='text-indent:20px;'>Huanglongbing (HLB) is a disease of citrus that caused by phloem-restricted bacteria of the Candidatus Liberibacter group. In this paper, we present a HLB transmission model to investigate the effects of temperature-dependent latent periods and seasonality on the spread of HLB. We first establish disease free dynamics in terms of a threshold value <inline-formula><tex-math id="M1">\begin{document}$ R^p_0 $\end{document}</tex-math></inline-formula>, and then introduce the basic reproduction number <inline-formula><tex-math id="M2">\begin{document}$ \mathcal{R}_0 $\end{document}</tex-math></inline-formula> and show the threshold dynamics of HLB with respect to <inline-formula><tex-math id="M3">\begin{document}$ R^p $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M4">\begin{document}$ \mathcal{R}_0 $\end{document}</tex-math></inline-formula>. Numerical simulations are further provided to illustrate our analytic results.</p>

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The Role of Migration in Maintaining the Transmission of Avian Influenza in Waterfowl: A Multisite Multispecies Transmission Model along East Asian-Australian Flyway

Canadian Journal of Infectious Diseases and Medical Microbiology ◽

10.1155/2018/3420535 ◽

2018 ◽

Vol 2018 ◽

pp. 1-7 ◽

Cited By ~ 1

Author(s):

Akira Endo ◽

Hiroshi Nishiura

Keyword(s):

Avian Influenza ◽

Reproduction Number ◽

Transmission Rate ◽

Temporal Variations ◽

Transmission Model ◽

Global Dynamics ◽

Long Distance ◽

Transmission Potential ◽

Influenza Transmission

Background. Migratory waterfowl annually migrate over the continents along the routes known as flyways, serving as carriers of avian influenza virus across distant locations. Prevalence of influenza varies with species, and there are also geographical and temporal variations. However, the role of long-distance migration in multispecies transmission dynamics has yet to be understood. We constructed a mathematical model to capture the global dynamics of avian influenza, identifying species and locations that contribute to sustaining transmission.Methods. We devised a multisite, multispecies SIS (susceptible-infectious-susceptible) model, and estimated transmission rates within and between species in each geographical location from prevalence data. Parameters were directly sampled from posterior distribution under Bayesian inference framework. We then analyzed contribution of each species in each location to the global patterns of influenza transmission.Results. Transmission and migration parameters were estimated by Bayesian posterior sampling. The basic reproduction number was estimated at 1.1, slightly above the endemic threshold. Mallard was found to be the most important host with the highest transmission potential, and high- and middle-latitude regions appeared to act as hotspots of influenza transmission. The local reproduction number suggested that the prevalence of avian influenza in the Oceania region is dependent on the inflow of infected birds from other regions.Conclusion. Mallard exhibited the highest transmission rate among the species explored. Migration was suggested to be a key factor of the global prevalence of avian influenza, as transmission is locally sustainable only in the northern hemisphere, and the virus could be extinct in the Oceania region without migration.

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Global dynamics of a pine wilt disease transmission model with nonlinear incidence rates

Applied Mathematical Modelling ◽

10.1016/j.apm.2012.09.042 ◽

2013 ◽

Vol 37 (6) ◽

pp. 4561-4569 ◽

Cited By ~ 14

Author(s):

Kwang Sung Lee ◽

Daewook Kim

Keyword(s):

Disease Transmission ◽

Pine Wilt Disease ◽

Incidence Rates ◽

Wilt Disease ◽

Transmission Model ◽

Global Dynamics ◽

Nonlinear Incidence ◽

Pine Wilt ◽

Nonlinear Incidence Rates ◽

Disease Transmission Model

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Freely-Moving Delay Induces Periodic Oscillations in a Structured SEIR Model

International Journal of Bifurcation and Chaos ◽

10.1142/s021812741750122x ◽

2017 ◽

Vol 27 (08) ◽

pp. 1750122 ◽

Cited By ~ 2

Author(s):

Yanfei Du ◽

Yuxiao Guo ◽

Peng Xiao

Keyword(s):

Periodic Solutions ◽

Disease Transmission ◽

Time Lag ◽

Stage Structure ◽

Transmission Model ◽

Positive Equilibrium ◽

Global Dynamics ◽

Asymptotically Stable ◽

Normal Form Theory ◽

Freely Moving

In this paper, a disease transmission model of SEIR type with stage structure is proposed and studied. Two kinds of time delays are considered: the first one is the mature delay which divides the population into two stages; the second one is the time lag between birth and being able to move freely, which we call the freely-moving delay. Our mathematical analysis establishes that the global dynamics are determined by the basic reproduction number [Formula: see text]. If [Formula: see text], then the disease free equilibrium [Formula: see text] is globally asymptotically stable, and the disease will die out. If [Formula: see text], then a unique positive equilibrium [Formula: see text] exists, and [Formula: see text] is locally asymptotically stable when the freely-moving delay is less than the critical value. We show that increasing this delay can destabilize [Formula: see text] and lead to Hopf bifurcations and stable periodic solutions. By using the normal form theory and the center manifold theory, we derive the formulae for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions. Finally, some numerical simulations are carried out to verify the theoretical analysis and some biological implications are discussed.

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