Dynamics of an SIR Model with Nonlinear Incidence and Treatment Rate
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| Title: | Dynamics of an SIR Model with Nonlinear Incidence and Treatment Rate |
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| Authors: | Dubey, Balram, Dubey, Preeti, Dubey, Uma S. |
| Source: | Applications and Applied Mathematics: An International Journal (AAM) |
| Publisher Information: | Digital Commons @PVAMU |
| Publication Year: | 2015 |
| Subject Terms: | SIR model, Beddington-DeAngelis type nonlinear incidence rate, Limit cycle, Hopf bifurcation, Next generation matrix method, Central manifold theory, Biology, Control Theory, Ordinary Differential Equations and Applied Dynamics, Other Physical Sciences and Mathematics |
| Description: | In this paper, global dynamics of an SIR model are investigated in which the incidence rate is being considered as Beddington-DeAngelis type and the treatment rate as Holling type II (saturated). Analytical study of the model shows that the model has two equilibrium points (diseasefree equilibrium (DFE) and endemic equilibrium (EE)). The disease-free equilibrium (DFE) is locally asymptotically stable when reproduction number is less than one. Some conditions on the model parameters are obtained to show the existence as well as nonexistence of limit cycle. Some sufficient conditions for global stability of the endemic equilibrium using Lyapunov function are obtained. The existence of Hopf bifurcation of model is investigated by using Andronov-Hopf bifurcation theorem. Further, numerical simulations are done to exemplify the analytical studies. |
| Document Type: | text |
| File Description: | application/pdf |
| Language: | unknown |
| Relation: | https://digitalcommons.pvamu.edu/aam/vol10/iss2/5; https://digitalcommons.pvamu.edu/context/aam/article/1446/viewcontent/05_dubey_aam_r833_bd_070815_edited_jv_r.pdf |
| Availability: | https://digitalcommons.pvamu.edu/aam/vol10/iss2/5 https://digitalcommons.pvamu.edu/context/aam/article/1446/viewcontent/05_dubey_aam_r833_bd_070815_edited_jv_r.pdf |
| Accession Number: | edsbas.E241521B |
| Database: | BASE |
Nájsť tento článok vo Web of Science | Abstract: | In this paper, global dynamics of an SIR model are investigated in which the incidence rate is being considered as Beddington-DeAngelis type and the treatment rate as Holling type II (saturated). Analytical study of the model shows that the model has two equilibrium points (diseasefree equilibrium (DFE) and endemic equilibrium (EE)). The disease-free equilibrium (DFE) is locally asymptotically stable when reproduction number is less than one. Some conditions on the model parameters are obtained to show the existence as well as nonexistence of limit cycle. Some sufficient conditions for global stability of the endemic equilibrium using Lyapunov function are obtained. The existence of Hopf bifurcation of model is investigated by using Andronov-Hopf bifurcation theorem. Further, numerical simulations are done to exemplify the analytical studies. |
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