An epidemic model of a vector-borne disease with direct transmission and time delay

Wei, Huiming; Li, Xuezhi; Martcheva, Maia

doi:10.1016/j.jmaa.2007.12.058

Cited by 117 publications

(85 citation statements)

References 44 publications

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“…Application of the conclusions of [17], we can know that positive z doesn't exist. Hence  also doesn't exist.…”

Section: The Stability Of Endemic Equilibriummentioning

confidence: 97%

Global Stability Analysis of a Delayed SEIQR Epidemic Model with Quarantine and Latent

Li¹,

Xue²

2013

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In this paper, we study a kind of the delayed SEIQR infectious disease model with the quarantine and latent, and get the threshold value which determines the global dynamics and the outcome of the disease. The model has a disease-free equilibrium which is unstable when the basic reproduction number is greater than unity. At the same time, it has a unique endemic equilibrium when the basic reproduction number is greater than unity. According to the mathematical dynamics analysis, we show that disease-free equilibrium and endemic equilibrium are locally asymptotically stable by using Hurwitz criterion and they are globally asymptotically stable by using suitable Lyapunov functions for any . Besides, the SEIQR model with nonlinear incidence rate is studied, and the 0  that the basic reproduction number is a unity can be found out. Finally, numerical simulations are performed to illustrate and verify the conclusions that will be useful for us to control the spread of infectious diseases. Meanwhile, the 1 , k 3 k will effect changing trends of , S , E , I , Q R in system (1), which is obvious in simulations. Here, we take 3 k as an example to explain that.

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“…Application of the conclusions of [17], we can know that positive z doesn't exist. Hence  also doesn't exist.…”

Section: The Stability Of Endemic Equilibriummentioning

confidence: 97%

Global Stability Analysis of a Delayed SEIQR Epidemic Model with Quarantine and Latent

Li¹,

Xue²

2013

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“…Los artrópodos presentan una gran capacidad adaptativa, que se manifiesta en su distribución cosmopolita, que favorece la diseminación y la presencia de arbovirus en gran parte del planeta. Los insectos vectores presentan un hábito hematófago, esencial para la producción de huevos y la oviposición, por lo que su capacidad reproductiva está muy influenciada por la frecuencia de la ingestión, lo cual favorece la capacidad de contacto entre los arbovirus y los hospedadores vertebrados (23)(24)(25)(26).…”

Section: Ciclo De Transmisión Del Virus Mayaro Artrópodos Vectoresunclassified

Virus Mayaro: un arbovirus reemergente en Venezuela y Latinoamérica

Múñoz

Navarro

2012

biomedica

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El virus Mayaro produce una enfermedad de síntomas inespecíficos y subletales, frecuentemente confundida con dengue, con síntomas de artralgias que pueden generar incapacidad laboral. Los brotes han sido esporádicos y localizados en la región selvática de la Panamazonia, posterior a su primer aislamiento en 1954 (Trinidad y Tobago). La información en la literatura científica es escasa, diversa y dispersa. El virus Mayaro es un alfavirus filogenéticamente relacionado con el complejo del virus Semliki Forest (SFV); con el UNA, son los únicos virus de dicho complejo aislados en el Nuevo mundo. Está conformado por ARN de cadena simple de carga positiva, con longitud de 12 kb con la región 42S y 26S, que codifican para proteínas no estructurales y estructurales. El virus Mayaro presenta gran adaptabilidad para la infección en vertebrados y especificidad hacia la familia Culicidae (mosquitos) como vectores u hospedadores invertebrados. Los factores de riesgo están asociados a zonas boscosas de la región septentrional de Suramérica y en temporada lluviosa. Se conocen dos genotipos, L (Belterra, Brasil) y D (distribución panamazónica). El ciclo enzoótico es similar al de la fiebre amarilla, que involucra a mosquitos del género Haemagogus y, como reservorios, a monos, sin descartar la participación de vectores secundarios y otros hospedadores que pudieran participar en la diseminación del virus. El humano puede presentar viremia elevada y se ha demostrado la transmisión experimental en Aedes aegypti, Ae. scapularis y Ae. albopictus, constituyendo un riesgo para la salud pública en centros urbanos y zonas rurales cercanas a focos de virus Mayaro.Palabras clave: Aedes, alfavirus, ecosistema amazónico, arbovirus, artralgia, filogenia, Culicidae, virus del bosque Semliki, Togaviridae Mayaro: A re-emerging Arbovirus in Venezuela and Latin AmericaMayaro virus produces nonspecific, sublethal disease symptoms, often confused with dengue, but with symptoms of arthalgias that can cause incapacitating disability. Outbreaks have been localized and sporadic in the Pan-Amazonia forest since its first isolation in 1954 (Trinidad and Tobago). The literature available is scarce, diverse and dispersed. Mayaro virus is an alphavirus, phylogenetically related to the Semliki forest antigenic complex. UNA and Mayaro viruses are the only viruses of this complex that have been isolated in the New World. Mayaro consists of single-stranded RNA of positive charge, length of 12 kb, subdivided into genomic and subgenomic regions, which encode nonstructural and structural proteins respectively. Mayaro shows a great plasticity in vertebrate host infection, whereas high specificity in the family Culicidae (mosquitoes). Risk factors of infection are associated with forest areas of northern South America and the rainy season. Two genotypes of MAYV have been identified, L (Belterra, Brazil) and D (widely distributed in the Pan-Amazonia). The enzootic cycle is similar to the jungle cycle of yellow fever, which involves Haemagogus mosquitoes and monkeys as ...

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“…For an equilibrium for which Equation (38) does not hold, we have f (0) < g(0) and for real λ as λ → ∞, f (λ) → ∞ while g(λ) → βS * , so the characteristic equation will have a positive real root. Such an equilibrium will be unstable.…”

Section: Human Influenza Equilibriummentioning

confidence: 99%

“…(38) holds can become unstable in the sense that Equation (35) can have complex solution λ with positive real part. In this case sustained oscillations are possible.…”

Section: Human Influenza Equilibriummentioning

confidence: 99%

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An evolutionary model of influenza A with drift and shift

Martcheva

2012

Journal of Biological Dynamics

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Influenza A virus evolves through two types of evolutionary mechanisms -drift and shift. These two evolutionary mechanisms allow the pathogen to infect us repeatedly, as well as occasionally create pandemics with large morbidity and mortality. Here we introduce a novel model that incorporates both evolutionary mechanisms. This necessitates the modelling of three types of strains -seasonal human strains, bird-to-human transmittable H5N1 strains and evolved pandemic H5N1 strain. We define reproduction and invasion reproduction numbers and use them to establish the presence of dominant and coexistence equilibria. We find that the amino acid substitution structure of human influenza can destabilize the human influenza equilibrium and sustained oscillations are possible. We find that for low levels of infection in domestic birds, these oscillations persist, inducing oscillations in the number of humans infected with the avian flu strain. The oscillations have a period of 365 days, similar to the one that can be observed in the cumulative number of human H5N1 cases reported by the World Health Organization (WHO). Furthermore, we establish some partial global results on the competition of the strains.

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An epidemic model of a vector-borne disease with direct transmission and time delay

Abstract: Journal of Mathematical Analysis and Applications 342 (2008) 895-908. doi:10.1016/j.jmaa.2007.12.058Received by publisher: 2007-06-21Harvest Date: 2016-01-04 12:20:16DOI: 10.1016/j.jmaa.2007.12.058Page Range: 895-90

Cited by 117 publications

References 44 publications

Global Stability Analysis of a Delayed SEIQR Epidemic Model with Quarantine and Latent

Global Stability Analysis of a Delayed SEIQR Epidemic Model with Quarantine and Latent

Virus Mayaro: un arbovirus reemergente en Venezuela y Latinoamérica

An evolutionary model of influenza A with drift and shift

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