Nonlinear Models for the Delayed Immune Response to a Viral Infection

Gleria, Iram; Neto, Adhemar Ranciaro; Canabarro, Askery

doi:10.1007/s13538-015-0339-6

Cited by 4 publications

(6 citation statements)

References 24 publications

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“…Note that the stability of the fixed points of a n-dimensional system with k delays can be analyzed using the usual Jacobian evaluated at the equilibrium point [11]. Eachẋ i , i = 1, · · · , n be writteṅ…”

Section: Resultsmentioning

confidence: 99%

“…Bifurcations occur whenever one eigenvalue crosses the imaginary axis as one or more parameters, including the delays, change. Typical bifurcations involve a turning point when the eigenvalue is initially null, and a Hopf bifurcation when a pair of complex eigenvalues crosses the imaginary axis [11]. The general expression for the Jacobian is…”

Section: Resultsmentioning

confidence: 99%

“…We used two coupled delayed equations to model the interaction of the immune system with a target population [5]. We used some analytical tools to analyze delayed systems [11], and we published new results for the model originally presented in Ref. [2].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A nonlinear delayed model for the immune response in the presence of viral mutation

Messias¹,

Gleria²,

Albuquerque³

et al. 2018

Physica A: Statistical Mechanics and its Applications

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

A nonlinear delayed model for the immune response in the presence of viral mutation

Messias¹,

Gleria²,

Albuquerque³

et al. 2018

Physica A: Statistical Mechanics and its Applications

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show abstract

“…Mathematical modelling is a recognized powerful tool to investigate transmission and epidemic dynamics [9][10][11][17][18][19][20][21][22]. Here, we present a data-driven and census-based age-structured mathematical epidemiological model capable of asserting the potential output of many NPI over the Brazillian health system by explicitly computing the basic reproduction rate R 0 , the evolution of the number of infections and the required quantity of ICUs needed over time.…”

Section: Introductionmentioning

confidence: 99%

Data-Driven Study of the COVID-19 Pandemic via Age-Structured Modelling and Prediction of the Health System Failure in Brazil amid Diverse Intervention Strategies

Canabarro

Tenório²,

Martins

et al. 2020

Preprint

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In this work we propose a data-driven age-structured census-based SIRD-like epidemiological model capable of forecasting the spread of COVID-19 in Brazil. We model the current scenario of closed schools and universities, social distancing of individuals above sixty years old and voluntary home quarantine to show that it led to a considerable reduction in the number of infections as compared with a scenario without any control measures. Notwithstanding, our model predicts that the current measures are not enough to avoid overloading the health system, since the demand for intensive care units will soon surpass the number available. We also show that an urgent intense quarantine might be the only solution to avoid this scenario and, consequently, minimize the number of severe cases and deaths. On the other hand, we demonstrate that the early relaxation of the undergoing isolation measures would lead to an increase of millions of infections in a short period of time and the consecutive collapse of the health system.

show abstract

“…Mathematical modelling is a recognized powerful tool to investigate transmission and epidemic dynamics [9][10][11][18][19][20][21][22][23][24]. Here, we present a data-driven and census-based age-structured mathematical epidemiological model capable of asserting the potential output of many NPI over the Brazillian health system by explicitly computing the basic reproduction rate R 0 , the evolution of the number of infections and the required quantity of ICUs needed over time.…”

Section: Introductionmentioning

confidence: 99%

Data-driven study of the COVID-19 pandemic via age-structured modelling and prediction of the health system failure in Brazil amid diverse intervention strategies

Canabarro

Tenório²,

Martins³

et al. 2020

PLoS ONE

Self Cite

View full text Add to dashboard Cite

In this work we propose a data-driven age-structured census-based SIRD-like epidemiological model capable of forecasting the spread of COVID-19 in Brazil. We model the current scenario of closed schools and universities, social distancing of people above sixty years old and voluntary home quarantine to show that it is still not enough to protect the health system by explicitly computing the demand for hospital intensive care units. We also show that an urgent intense quarantine might be the only solution to avoid the collapse of the health system and, consequently, to minimize the quantity of deaths. On the other hand, we demonstrate that the relaxation of the already imposed control measures in the next days would be catastrophic.

show abstract

Nonlinear Models for the Delayed Immune Response to a Viral Infection

Cited by 4 publications

References 24 publications

A nonlinear delayed model for the immune response in the presence of viral mutation

A nonlinear delayed model for the immune response in the presence of viral mutation

Data-Driven Study of the COVID-19 Pandemic via Age-Structured Modelling and Prediction of the Health System Failure in Brazil amid Diverse Intervention Strategies

Data-driven study of the COVID-19 pandemic via age-structured modelling and prediction of the health system failure in Brazil amid diverse intervention strategies

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