The risk of yellow fever in a dengue-infested area

Massad, Eduardo; Coutinho, Francisco Antônio Bezerra; Burattini, Marcelo Nascimento; López, Luis Fernández

doi:10.1016/s0035-9203(01)90184-1

Cited by 124 publications

(133 citation statements)

References 7 publications

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“…By outbreak we understand the sudden exponential rise in the number of cases in the beginning of the transmission season. The list of those 61 cities can be seen in Table. The calculation of R 0 can be carried out from the initial exponential growing phase of the number of cases as detailed in Massad et al (2001). However, we show in the appendix a summary of the derivation of R 0 and λ.…”

Section: Methodsmentioning

confidence: 99%

“…By fitting the proportion of new cases to an exponential curve, we can estimate R 0 . The values of the parameters were µ = 0.156 weeks -1 and γ = 1 week -1 (Massad et al 2001).…”

Section: Methodsmentioning

confidence: 99%

“…Dengue fever (DF), a Flaviridae infection transmitted by peridomestic Aedes aegypti (Gubler & Kuno 1997) re-appeared as a major urban epidemic in Brazil in 1986 (Marques et al 1994, Massad et al 2001, Luz et al 2003 and is currently the most important arthropodborne viral disease in Brazil (Luz et al 2003). By the year 2000, all 26 states had reported DF cases.…”

mentioning

confidence: 99%

“…Let also S m and I m be number of susceptible and infectious individuals, respectively, in a mosquito population. We can write (Massad et al 2001): (1)…”

mentioning

confidence: 99%

“…Remembering that R 0 is (6) R 0 = ------------ma 2 bexp(μ λ) γ μ Therefore, from equations (5) and (6) we obtain (Massad et al 2001):…”

mentioning

confidence: 99%

See 4 more Smart Citations

Dynamics of the 2006/2007 dengue outbreak in Brazil

Coelho

Burattini

Teixeira

et al. 2008

Mem. Inst. Oswaldo Cruz

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Section: Methodsmentioning

confidence: 99%

“…By fitting the proportion of new cases to an exponential curve, we can estimate R 0 . The values of the parameters were µ = 0.156 weeks -1 and γ = 1 week -1 (Massad et al 2001).…”

Section: Methodsmentioning

confidence: 99%

mentioning

confidence: 99%

“…Let also S m and I m be number of susceptible and infectious individuals, respectively, in a mosquito population. We can write (Massad et al 2001): (1)…”

mentioning

confidence: 99%

“…Remembering that R 0 is (6) R 0 = ------------ma 2 bexp(μ λ) γ μ Therefore, from equations (5) and (6) we obtain (Massad et al 2001):…”

mentioning

confidence: 99%

See 3 more Smart Citations

Dynamics of the 2006/2007 dengue outbreak in Brazil

Coelho

Burattini

Teixeira

et al. 2008

Mem. Inst. Oswaldo Cruz

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Modeling the spread of hepatitis C virus amongst people who inject drugs

Greenhalgh

Al‐Rashidi

2022

Engineering Reports

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This article discusses two models, with two different needle assumptions for the transmission of hepatitis C virus (HCV) between people who inject drugs (PWIDs) who share needles and syringes. Our analysis demonstrates that the basic reproduction number R0 determines how the model behaves. R0=1 is a crucial threshold parameter which divides two qualitatively different scenarios. It has been shown that if R0≤1 only a disease‐free equilibrium point exists. On the other hand if R0>1 a unique endemic equilibrium point exists as well as the disease‐free one. The disease‐free equilibrium point is globally asymptotically stable if R0≤1 otherwise unstable. We look at an approximation to this model by using the fact that the timescale on which the individual PWIDs inject with needles or syringes is much faster than the timescale of epidemiological change. Also, we showed that if R0>1 the endemic equilibrium point is locally asymptotically stable for our approximation to this model. Additionally, we perform some simulations with realistic parameter values which confirm that if R0>1 then the solutions to this model tend to this endemic equilibrium value giving a steady‐state nonzero HCV prevalence. With realistic parameter values for both assumptions we find that R0=2.9987 and the total endemic equilibrium fraction of infectious PWIDs is 0.5348 and the total equilibrium fraction of antibody positive PWIDs is 0.65. The total fraction of infectious needles is 0.275.

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Incorporation of awareness programs into a model of the spread of HIV/AIDS among people who inject drugs

Alsharari

Greenhalgh

2022

Engineering Reports

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Mathematical modeling techniques have been used extensively during the human immunodeficiency virus (HIV) epidemic. Drug injection causes increased HIV spread in most countries globally. The media is crucial in spreading health awareness by changing mixing behavior. The published studies show some of the ways that differential equation models can be employed to explain how media awareness programs influence the spread and containment of disease (Greenhalgh et al. Appl Math Comput. 2015;251:539-563). Here we build a differential equation model which shows how disease awareness programs can alter the HIV prevalence in a group of people who inject drugs (PWIDs). This builds on previous work by Greenhalgh and Hay (1997) and Liang et al. (2016).We have constructed a mathematical model to describe the improved model that reduces the spread of the diseases through the effect of awareness of disease on sharing needles and syringes among the PWID population. The model supposes that PWIDs clean their needles before use rather than after. We carry out a steady state analysis and examine local stability. Our discussion has been focused on two ways of studying the influence of awareness of infection levels in epidemic modeling. The key biological parameter of our model is the basic reproductive number R 0 . R 0 is a crucial number which determines the behavior of the infection. We find that if R 0 is less than one then the disease-free steady state is the unique steady state and moreover whatever the initial fraction of infected individuals then the disease will die out as time becomes large. If R 0 exceeds one there is the disease-free steady state and a unique steady state with disease present. We also showed that the disease-free steady state is locally asymptotically stable if R 0 is less than one, neutrally stable if R 0 is equal to one and unstable if R 0 exceeds one. In the last case, when R 0 is greater than one the endemic steady state was locally asymptotically stable. Our analytical results are confirmed by using simulation with realistic parameter values. In nontechnical terms, the number R 0 is a critical value describing how the disease will spread.

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The risk of yellow fever in a dengue-infested area

Cited by 124 publications

References 7 publications

Dynamics of the 2006/2007 dengue outbreak in Brazil

Dynamics of the 2006/2007 dengue outbreak in Brazil

Modeling the spread of hepatitis C virus amongst people who inject drugs

Incorporation of awareness programs into a model of the spread of HIV/AIDS among people who inject drugs

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