Global dynamics of a dengue epidemic mathematical model

Cai, Liming; Guo, Shougang; Li, Xuezhi; Ghosh, Mini

doi:10.1016/j.chaos.2009.03.130

Cited by 60 publications

(33 citation statements)

References 17 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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“…As mentioned and motivated in the previous section, we assume that there is a saturating effect of diseases transmissions when the number of infectious (humans and mosquitoes) becomes large enough [6,7,31]. Therefore, we adopt Holling II Holling II parameter for infectious mosquitoes 0.3 Table 1: Description and baseline values of parameters in system (2).…”

Section: The Model Basic Properties and Disease-free Statesmentioning

confidence: 99%

“…and m * and a * are given by (6). The characteristic polynomial of the Jacobian matrix corresponding to (1) evaluated at E 1 is a fifth-degree polynomial.…”

Section: Endemic Equilibriummentioning

confidence: 99%

“…In particular, for vector-host epidemics, there are several biological mechanisms which may result in nonlinearities in the transmission rates of parasites [7]. For this reason, several authors have recently proposed nonlinear forces of infection for vector-host epidemics, for one or both the transmissions (from vector to host and viceversa) [5,6,7,18,31].…”

Section: Introductionmentioning

confidence: 99%

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Analysis of a mosquito-borne disease transmission model with vector stages and nonlinear forces of infection

Ávila-Vales

Buonomo

2015

Ricerche mat.

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We study a mosquito-borne epidemic model where the vector population is distinct in aquatic and adult stages and a saturating effect of disease transmission is assumed to occur when the number of infectious (humans and mosquitoes) becomes large enough. Several techniques, including center manifold analysis and sensitivity analysis, have been used to reveal relevant features of the model dynamics. We determine the existence of stability-instability thresholds and the individual role played in such thresholds by the model parameters.

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“…In most of the epidemiological models, the incidence rate is assumed of the form βSI, where β is the transmission rate, S and I are the susceptible and infected population respectively. Cai et al [14] used a saturated incidence rate of the form bβSI/(1 + αI) where b, β, α > 0.…”

Section: Introductionmentioning

confidence: 99%