The basic reproduction number obtained from Jacobian and next generation matrices – A case study of dengue transmission modelling

Yang, Hyun Mo

doi:10.1016/j.biosystems.2014.10.002

Cited by 85 publications

(86 citation statements)

References 26 publications

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“…The next generation matrix, evaluated at the trivial equilibrium P 0 , is obtained considering the vector of variables x = (e y , a y , d 1y , e o , a o , d 1o ). We apply method proposed in [15] and proved in [16]. There are control mechanisms (isolation), hence we obtain the reduced reproduction number R r by isolation.…”

Section: Resultsmentioning

confidence: 99%

“…where the superscript T stands for the transposition of a matrix, from which we obtain the matrices F and V (see [4]) evaluated at the trivial equilibrium P 0 , which were omitted. The next generation matrix F V −1 is where the basic reproduction number R 0 is Instead of using the spectral radius (ρ (F V −1 ) = √ R 0 ), we apply procedure in [15] (the sum of coefficients of characteristic equation), resulting in a threshold R 0 . Hence, the trivial equilibrium point P 0 is locally asymptotically stable (LAS) if R 0 < 1.…”

Section: Resultsmentioning

confidence: 99%

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Mathematical model describing CoViD-19 in São Paulo State, Brazil – Evaluating isolation as control mechanism and forecasting epidemiological scenarios of release

Yang

Lombardi

Castro

et al. 2020

Preprint

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We formulated a mathematical model considering young (below 60 years old) and elder (above 60 years) subpopulations to describe the introduction and dissemination of new coronavirus epidemics in the São Paulo State, Brazil. From the data collected in São Paulo State, we estimated the model parameters and calculated the basic reproduction number as R 0 = 6.828. Considering isolation as a control mechanism, we varied the releasing proportions of young and elder persons to assess their epidemiological impacts. The best scenarios were release of young persons, but maintaining elder persons isolated. To avoid the collapse of the health care system, the isolation must be at least 80%.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Mathematical model describing CoViD-19 in São Paulo State, Brazil – Evaluating isolation as control mechanism and forecasting epidemiological scenarios of release

Yang

Lombardi

Castro

et al. 2020

Preprint

Self Cite

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show abstract

“…Evaluating the next generation matrix F 1 V −1 , the corresponding characteristic equation is 11) and applying the conjecture proposed in [13], the threshold is R h R m , which is the same obtained in the previous construction of vectors f and v, given by Eq. (3.10).…”

Section: Next Generation Matrix Methodsmentioning

confidence: 99%

“…The conjecture presented in [13] says that the spectral radius is not the basic reproduction number, but it is the geometric mean of the partial reproduction numbers.…”

Section: Next Generation Matrix Methodsmentioning

confidence: 99%

Comparison between chikungunya and dengue viruses transmission based on a mathematical model

Yang

2017

Int. J. Biomath.

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Chikungunya and dengue viruses are transmitted by mosquitoes of genus Aedes. Based on a mathematical model dealing with arboviruses transmission that encompasses human and mosquito populations, the risks of dengue and chikungunya infections are compared. By the fact that chikungunya virus attains high viral load earlier than dengue virus in both humans and mosquitoes, the potential risk of chikungunya could be higher than the dengue infection. The risk of arboviruses infections is assessed by the reproduction number [Formula: see text], which is obtained by the next generation matrix method and Routh–Hurwitz criteria.

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“…e basic reproduction number (R 0 ) is the expected average number of new TB infections caused by a single infected individual when in contact with a completely susceptible population. We obtained R 0 by using the next-generation matrix method given in [17], this amounts to calculating the two matrices and , where is the rate of transfer of individuals into and out of the infected classes and is the rate of new infections in the compartment. Hence, by the equations we obtain,…”

Section: Invariant Regions Eorem 2 With the Nonnegative Initial Condmentioning

confidence: 99%

Modeling the Effects of Vaccination and Treatment on Tuberculosis Transmission Dynamics

Mengistu

Witbooi

2019

Journal of Applied Mathematics

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In this study, we develop and analyze a deterministic mathematical model for tuberculosis (TB) transmission dynamics. e model includes vaccination for newborns and treatment for both high-risk latent and active TB patients. e stability of disease-free equilibrium point is discussed in detail. In the numerical simulation, the model parameters are estimated using reported TB incidence data in Ethiopia from the years 2003 to 2017, and R 0 is calculated as R 0 ≈ 2.13. Finally, the sensitivity indices of R 0 with respect to the model parameters are performed, and their corresponding graphical results are presented. Our results quantify the positive in uence of vaccination and the treatment for high-risk latent and active TB patients on the control of tuberculosis.

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The basic reproduction number obtained from Jacobian and next generation matrices – A case study of dengue transmission modelling

Cited by 85 publications

References 26 publications

Mathematical model describing CoViD-19 in São Paulo State, Brazil – Evaluating isolation as control mechanism and forecasting epidemiological scenarios of release

Mathematical model describing CoViD-19 in São Paulo State, Brazil – Evaluating isolation as control mechanism and forecasting epidemiological scenarios of release

Comparison between chikungunya and dengue viruses transmission based on a mathematical model

Modeling the Effects of Vaccination and Treatment on Tuberculosis Transmission Dynamics

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