Rich dynamics of an SIR epidemic model

Pathak, Shivang; Maiti, Alakes; Samanta, G. P.

doi:10.15388/na.2010.15.1.14365

Cited by 52 publications

(37 citation statements)

References 29 publications

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“…After further study we can understand that it directly related to number of deceased and infected population, so therefore finding the rate of infection and dead by the disease will clearly to some extent determine γ i.e. removed parameter [12]. Further the following Table 3, will give us better indication of the above parameters and how significantly they affect the output.…”

Section: E Forecasting Of Covid-19 Using Sir Modelmentioning

confidence: 95%

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Short Term Nowcasting and Forecasting for COVID-19 Potential Spread in SAARC Country: A Modeling Study Using Machine Learning Approach

Nanda¹

2020

IJRASET

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Emergence of infectious diseases, such as severe acute respiratory syndrome (SARS) and Zika virus disease have presented a major threat to public health. Despite intense research efforts, when and where new diseases appear are still a source of considerable uncertainty. As the COVID-19 has strike globally and form as a large scale pandemic disease in a very short phase. So understanding the severity of the disease to estimate the case fatality risk is a common epidemiological practice defined as the risk of death among cases. The ongoing COVID-19 pandemic continues to spread globally and stating about SAARC countries, the spread is not that alarming to panic, as several social distancing measures implemented by different SAARC governments, but still it is not in the situation of negligence and slackness. We have used forecast models i.e. ARIMA model and SIR Model to generate the short term forecasts of the COVID-19 spread in SAARC countries i.e. India, Afghanistan, Sri-Lanka, Maldives, Bhutan, Pakistan, Nepal and Bangladesh using daily reported number of case from 22 January, 2020 up to 01 April , 2020, the forecast for each countries have been generated separately but for the validation we have used forecast of whole SAARC and values are really good for prediction as ARIMA(0,2,3) is best fitted for confirmed cases with MAPE of 17.1, similarly ARIMA (0,2,1) for Death cases with excellent MAPE of 5.5 and lastly ARIMA(0,2,1 8.1, which is very good, the prediction is shows rise of confirm cases to 35000, death tolls to 600 and recovery to 1600 till 30 th April, 2020. For the SIR Model for SAARC, the trend is comes to peak of Infection during 95 th to 120 th day of the pandemic period with β=0.25 and γ=0.007. ) for Recovery cases with MAPE of

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Section: E Forecasting Of Covid-19 Using Sir Modelmentioning

confidence: 95%

“…Second, the population is homogenous (all individuals are the same) and only differ by their disease state. Third, infection and that individual's "infectiveness" or ability to infect susceptible individuals, occurs simultaneously [12].…”

Section: ) Sir Modelmentioning

confidence: 99%

Short Term Nowcasting and Forecasting for COVID-19 Potential Spread in SAARC Country: A Modeling Study Using Machine Learning Approach

Nanda¹

2020

IJRASET

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“…Also, we formulate an optimal control problem in order to minimize the number of breast cancer cells and amount of drugs used in the treatment. Other authors have studied similar problem .…”

Section: Introductionmentioning

confidence: 97%

Optimal control of a delayed breast cancer stem cells nonlinear model

Barrea

Hernández

2015

Optim. Control Appl. Meth.

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Summary In this article, we consider a nonlinear model, which is governed by an ordinary differential equations system with time delays in state and control. The model is used in order to describe the growth of breast cancer cells under therapy. We seek optimal therapies to minimize the number of cancer cells as well as the total quantity of drug used in the treatment. In this way, we formulate an optimal control problem. We prove the existence of an optimal therapy and use Pontryagin's maximum principle in order to find optimality conditions, which characterize such optimal therapy. At last, both numerical results and conclusion are presented. Copyright © 2015 John Wiley & Sons, Ltd.

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“…The fundamental characteristic of this model is: The modified saturated incidence rate βS(t)I(t)/(1 + α 1 S(t) + α 2 I(t)) (see, for example, [8][9][10]), which includes the three forms:…”

Section: Introductionmentioning

confidence: 99%

Optimal control of an epidemic model with a saturated incidence rate

Laarabi

Labriji

Rachik

et al. 2012

NAMC

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In this study we consider a mathematical model of an SIR epidemic model with a saturated incidence rate. We used the optimal vaccination strategies to minimize the susceptible and infected individuals and to maximize the number of recovered individuals. We work in the nonlinear optimal control framework. The existence result was discussed. A characterization of the optimal control via adjoint variables was established. We obtained an optimality system that we sought to solve numerically by a competitive Gauss–Seidel like implicit difference method.

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Rich dynamics of an SIR epidemic model

Cited by 52 publications

References 29 publications

Short Term Nowcasting and Forecasting for COVID-19 Potential Spread in SAARC Country: A Modeling Study Using Machine Learning Approach

Short Term Nowcasting and Forecasting for COVID-19 Potential Spread in SAARC Country: A Modeling Study Using Machine Learning Approach

Optimal control of a delayed breast cancer stem cells nonlinear model

Optimal control of an epidemic model with a saturated incidence rate

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