Complex Dynamics of an SIR Epidemic Model with Saturated Incidence Rate and Treatment

Jana, Soovoojeet; Nandi, Swapan Kumar; Kar, Tapan Kumar

doi:10.1007/s10441-015-9273-9

Cited by 61 publications

(28 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Exhibition of transcritical and backward bifurcation have been analysed in our work. It is important to mention here that our work is different from some of the other related works cited in this paper [10][11] because the stability or instability of endemic equilibrium point(s) is analysed by applying different techniques described in [12]. It should also be noted that in this paper, we shall deal with the qualitative analysis of the model as well as the optimal control of the disease.…”

Section: Introductionmentioning

confidence: 94%

“…To justify the impact of optimal control, we have used the forward-backward sweep method to solve the optimality system numerically. This method combines the forward application of a fourth order Runge-Kutta method for the state system (1) with the backward application of a fourth order Runge-Kutta method for the adjoint system (9) and the transversality conditions (10). Here, we fixed up our problem for 20 months and assume that the vaccination and treatment are stopped after 20 months.…”

Section: Numerical Simulations and Efficiency Analysismentioning

confidence: 99%

“…It is often used in the control of the spread of most infectious diseases for which either vaccine or treatment is available. Some researchers considered only vaccination control to their models [9] and some of them used only treatment control [9][10]. The author in [11] have used both the controls in their models.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Qualitative Analysis and Optimal Control Strategy of an SIR Model with Saturated Incidence and Treatment

Ghosh¹,

Ghosh

Biswas

et al. 2019

Differ Equ Dyn Syst

View full text Add to dashboard Cite

This paper deals with an SIR model with saturated incidence rate affected by inhibitory effect and saturated treatment function. Two control functions have been used, one for vaccinating the susceptible population and other for the treatment control of infected population. We have analysed the existence and stability of equilibrium points and investigated the transcritical and backward bifurcation. The stability analysis of non-hyperbolic equilibrium point has been performed by using Centre manifold theory. The Pontryagin's maximum principle has been used to characterize the optimal control whose numerical results show the positive impact of two controls mentioned above for controlling the disease. Efficiency analysis is also done to determine the best control strategy among vaccination and treatment.Mathematics Subject Classification: 37N25.34C23.49J15.92D30

show abstract

Section: Introductionmentioning

confidence: 94%

Section: Numerical Simulations and Efficiency Analysismentioning

confidence: 99%

See 1 more Smart Citation

Qualitative Analysis and Optimal Control Strategy of an SIR Model with Saturated Incidence and Treatment

Ghosh¹,

Ghosh

Biswas

et al. 2019

Differ Equ Dyn Syst

View full text Add to dashboard Cite

show abstract

“… 2014 ; Jana et al. 2016 , 2017a ). In his book, Murray ( 2002 ) has analysed theoretical works on some simple SI , SIS , SIR epidemic models.…”

Section: Introductionmentioning

confidence: 99%

Modelling and control of a fractional-order epidemic model with fear effect

Mandal

Jana²,

Nandi³

et al. 2020

Energ. Ecol. Environ.

Self Cite

View full text Add to dashboard Cite

In this paper, we formulate and study a new fractional-order SIS epidemic model with fear effect of an infectious disease and treatment control. The existence and uniqueness, nonnegativity and finiteness of the system solutions for the proposed model have been analysed. All equilibria of the model system are found, and their local and also global stability analyses are examined. Conditions for fractional backward and fractional Hopf bifurcation are also analysed. We study how the disease control parameter, level of fear and fractional order play a role in the stability of equilibria and Hopf bifurcation. Further, we have established our analytical results through several numerical simulations.

show abstract

“…Agrawal [21], in their study, they used a particular rate function which was not linear in nature. An epidemic model (SIR) with treatment function and rate of infection was described by [9]. In their study they focused on stability and set the dynamics of the model accordingly to build a basic reproduction number R0.…”

Section: Introductionmentioning

confidence: 99%

An Intelligent Prediction Model of COVID-19 in India using Hybrid Epidemic Model

Kumar

Bareja

Singh

et al. 2020

2020 International Conference on Smart Electronics and Communication (ICOSEC)

View full text Add to dashboard Cite

This article presents the current situation of COVID 19 spread in India and how it is impacted by various measures taken by the administration. Data source is taken (till 15th June 2020) from World Health Organization (WHO) to study various trends and pattern. Hybrid epidemic susceptible-infected recovered model is used to make predictions at every stage of coronavirus. The basic reproduction number R0, is constructed using a logistic function. An improved or hybrid epidemic model is build based on various other factors to build a logistic infection rate to analyse the patterns and trend in the data. Secondly, ICU beds and ventilators available per 100,000 inhabitants is also taken in account for critical. Also, the timeline for changing the stage of coronavirus is used from various reliable resources. Moreover, in comparison with the traditional SIR models, accuracy in the predictions has significantly increased with the R 2 value of 96.8 percent for the future days in India.

show abstract

Complex Dynamics of an SIR Epidemic Model with Saturated Incidence Rate and Treatment

Cited by 61 publications

References 30 publications

Qualitative Analysis and Optimal Control Strategy of an SIR Model with Saturated Incidence and Treatment

Qualitative Analysis and Optimal Control Strategy of an SIR Model with Saturated Incidence and Treatment

Modelling and control of a fractional-order epidemic model with fear effect

An Intelligent Prediction Model of COVID-19 in India using Hybrid Epidemic Model

Contact Info

Product

Resources

About