Global stability of an epidemic model for vector-borne disease

Yang, Haitao; Wei, Huiming; Li, Xuezhi

doi:10.1007/s11424-010-8436-7

Cited by 28 publications

(24 citation statements)

References 26 publications

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“…This model seems to be first suggested in [6,15] and it is now known as the Bailey-Dietz model. The global dynamics of this model was first studied in [18] using a Lyapunov function argument for the stability of the DFE, while the Poincaré-Bendixson property for 3-D competitive systems is used to show the stability of the EE; see also [8,89] for later similar studies. A global stability analysis using only Lyapunov functions has been obtained only recently- [74].…”

Section: Disease Dynamicsmentioning

confidence: 99%

On the dynamics of a class of multi-group models for vector-borne diseases

Iggidr

Sallet

Souza

2016

Journal of Mathematical Analysis and Applications

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Abstract. The resurgence of vector-borne diseases is an increasing public health concern, and there is a need for a better understanding of their dynamics. For a number of diseases, e.g. dengue and chikungunya, this resurgence occurs mostly in urban environments, which are naturally very heterogeneous, particularly due to population circulation. In this scenario, there is an increasing interest in both multi-patch and multigroup models for such diseases. In this work, we study the dynamics of a vector borne disease within a class of multi-group models that extends the classical Bailey-Dietz model. This class includes many of the proposed models in the literature, and it can accommodate various functional forms of the infection force. For such models, the vector-host/host-vector contact network topology gives rise to a bipartite graph which has different properties from the ones usually found in directly transmitted diseases. Under the assumption that the contact network is strongly connected, we can define the basic reproductive number R 0 and show that this system has only two equilibria: the so called disease free equilibrium (DFE); and a unique interior equilibrium-usually termed the endemic equilibrium (EE)-that exists if, and only if, R 0 > 1. We also show that, if R 0 ≤ 1, then the DFE equilibrium is globally asymptotically stable, while when R 0 > 1, we have that the EE is globally asymptotically stable.

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Section: Disease Dynamicsmentioning

confidence: 99%

On the dynamics of a class of multi-group models for vector-borne diseases

Iggidr

Sallet

Souza

2016

Journal of Mathematical Analysis and Applications

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“…Wei discussed the global stability of an epidemic model for vector-borne disease and they showed that the global dynamics are completely determined by the basic reproductive number R 0 [39]. Belayneh, et al provided a cost effective control effort for treatment of hosts and prevention of vector-host contacts for a non-autonomous model, while they establish global stability conditions for the autonomous case [6].…”

Section: Yanzhao Cao and Dawit Denumentioning

confidence: 99%

Analysis of stochastic vector-host epidemic model with direct transmission

Cao¹,

Denu²

2016

DCDS-B

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In this paper, we consider the stochastic vector-host epidemic model with direct transmission. First, we study the existence of a positive global solution and stochastic boundedness of the system of stochastic differential equations which describes the model. Then we introduce the basic reproductive number R s 0 in the stochastic model, which reflects the deterministic counterpart, and investigate the dynamics of the stochastic epidemic model when R s 0 < 1 and R s 0 > 1. In particular, we show that random effects may lead to extinction in the stochastic case while the deterministic model predicts persistence. Additionally, we provide conditions for the extinction of the infection and stochastic stability of the solution. Finally, numerical simulations are presented to illustrate some of the theoretical results.

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“…Remark 3.3 It is worth mentioning that Yang et al (2010) studied a similar vector-host epidemic model with an SIR structure for the host population and without disease-induced host deaths. They used the method of the second additive compound matrix (see Li and Muldowney 1996 and references therein) to establish the global stability of the endemic equilibrium when it exists.…”

Section: Mathematical Analysismentioning

confidence: 99%

Modeling the Spatial Spread of Rift Valley Fever in Egypt

et al. 2013

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Rift Valley fever (RVF) is a severe viral zoonosis in Africa and the Middle East that harms both human health and livestock production. It is believed that RVF in Egypt has been repeatedly introduced by the importation of infected animals from Sudan. In this paper, we propose a three-patch model for the process by which animals enter Egypt from Sudan, are moved up the Nile, and then consumed at population centers. The basic reproduction number for each patch is introduced and then the threshold dynamics of the model are established. We simulate an interesting scenario showing a possible explanation of the observed phenomenon of the geographic spread of RVF in Egypt.

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Global stability of an epidemic model for vector-borne disease

Cited by 28 publications

References 26 publications

On the dynamics of a class of multi-group models for vector-borne diseases

On the dynamics of a class of multi-group models for vector-borne diseases

Analysis of stochastic vector-host epidemic model with direct transmission

Modeling the Spatial Spread of Rift Valley Fever in Egypt

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