Stability Analysis of SEIR Model with Saturated Incidence and Time Delay

Tipsri, S.; Chinviriyasit, Wirawan

doi:10.7763/ijapm.2014.v4.252

Cited by 22 publications

(8 citation statements)

References 9 publications

(5 reference statements)

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“…As mentioned by Tipsri and Chinviriyasit [78] , the equilibrium solutions are same for the system with and without time delay. Therefore, to obtain the equilibrium points, we use

.…”

Section: Dynamics Of Delayed System (22)mentioning

confidence: 67%

Optimal control strategies to combat COVID-19 transmission: A mathematical model with incubation time delay

Singh

Bhatia

Bahri

et al. 2022

Results in Control and Optimization

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“…As mentioned by Tipsri and Chinviriyasit [78] , the equilibrium solutions are same for the system with and without time delay. Therefore, to obtain the equilibrium points, we use

.…”

Section: Dynamics Of Delayed System (22)mentioning

confidence: 67%

Optimal control strategies to combat COVID-19 transmission: A mathematical model with incubation time delay

Singh

Bhatia

Bahri

et al. 2022

Results in Control and Optimization

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“…Kermack and McKendrick [1,2] systematically introduced deterministic models for infectious diseases. Several researchers have explored different types of epidemic systems by examining the different models like SI [3], SIS [4], SIR [5,6,7,8,9,10], SIRS [9], SEIR [11,12,13,14], SIQR [15], SEIRV [16,17], etc to better understand the process of disease transmission. In recent decades, controlling infectious illnesses has become a more difficult task.…”

Section: Introductionmentioning

confidence: 99%

Study of a fractional order SIR model with M-H typetreatment rate and its stability analysis

Paul¹,

Mahata²,

Mukherjee³

et al. 2023

Preprint

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he fractional order SIR compartmental model with a Holling type II and saturated treatment rate are explored in this manuscript with three different categoriesin the Caputo approach. A few findings for the new model’s existence and uniqueness criterion, as well as non-negativity and boundedness of the solution, have beenestablished. The stability analysis of the model shows that the system is locallyas well as globally asymptotically stable at disease-free equilibrium point E0 when R0 < 1 and at epidemic equilibrium E1 when R0 > 1. We also present an optimumcontrol scheme for an SIR model using the control parameter “Treatment rate”. Inaddition, the fractional-order Taylor’s approach is utilized to approximate the solution to the proposed model. With the help of MATLAB, we were able to conductgraphical demonstrations and numerical simulations.

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“…In recent years, controlling infectious diseases has become a more di cult task [13]. Vaccination is one approach for controlling infectious diseases [14]. Vaccination is an important component of health treatments aiming at avoiding the spread of transferable diseases because of its wellbeing and rate e ciency [15].…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Analysis of SVIRS Disease System with Holling Type-II Saturated Incidence Rate and Saturated Treatment

Zhang

Madhusudanan²,

Murthy

et al. 2022

Mathematical Problems in Engineering

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This article presents a fuzzy SVIRS disease system with Holling type-II saturated incidence rate and saturated treatment, in which all parameters related to population dynamics have been considered as fuzzy numbers. Then, the existence condition and permanence of the SVIRS model have been discussed and we derived disease-free and endemic equilibrium points of the proposed fuzzy system. The local stability conditions of the fuzzy system around these equilibrium points using Routh–Hurwitz criteria are discussed. We also verified global stability around the interior steady state using Lozinskii measure. Computer simulations are provided to understand the dynamics of the proposed system. Parameter analysis is carried out with the help of computer simulation. Fuzzy provides better solution for any disease modeling in many ways like disease detection and transmission, different stages of disease, risk analysis (through parameter analysis), and optimal recovery solutions. Earlier literature acts as background to startup this disease modeling and optimal solutions provided by fuzzy logic is one of the motivational key element behind this fuzzy SVIRS model with Holling type-II and its analysis by both analytical and computer simulation.

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Stability Analysis of SEIR Model with Saturated Incidence and Time Delay

Cited by 22 publications

References 9 publications

Optimal control strategies to combat COVID-19 transmission: A mathematical model with incubation time delay

Optimal control strategies to combat COVID-19 transmission: A mathematical model with incubation time delay

Study of a fractional order SIR model with M-H typetreatment rate and its stability analysis

Fuzzy Analysis of SVIRS Disease System with Holling Type-II Saturated Incidence Rate and Saturated Treatment

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