Qualitative analysis and optimal control of an SIR model with logistic growth, non-monotonic incidence and saturated treatment

Ghosh, Jayanta K.; Majumdar, Prahlad; Ghosh, Uttam

doi:10.1051/mmnp/2021004

Cited by 12 publications

(2 citation statements)

References 27 publications

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“…There have been many studies (Zhang and Liu 2008 ; Zhang and Suo 2010 ; Ghosh et al. 2021 ; Jana et al. 2016 ; Zhou and Meng 2012 ) that used the saturated treatment function to characterize limited medical resources.…”

Section: Introductionmentioning

confidence: 99%

An SIRS model with nonmonotone incidence and saturated treatment in a changing environment

2022

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Nonmonotone incidence and saturated treatment are incorporated into an SIRS model under constant and changing environments. The nonmonotone incidence rate describes the psychological or inhibitory effect: when the number of the infected individuals exceeds a certain level, the infection function decreases. The saturated treatment function describes the effect of infected individuals being delayed for treatment due to the limitation of medical resources. In a constant environment, the model undergoes a sequence of bifurcations including backward bifurcation, degenerate Bogdanov-Takens bifurcation of codimension 3, degenerate Hopf bifurcation as the parameters vary, and the model exhibits rich dynamics such as bistability, tristability, multiple periodic orbits, and homoclinic orbits. Moreover, we provide some sufficient conditions to guarantee the global asymptotical stability of the disease-free equilibrium or the unique positive equilibrium. Our results indicate that there exist three critical values and for the treatment rate r : (i) when , the disease will disappear; (ii) when , the disease will persist. In a changing environment, the infective population starts along the stable disease-free state (or an endemic state) and surprisingly continues tracking the unstable disease-free state (or a limit cycle) when the system crosses a bifurcation point, and eventually tends to the stable endemic state (or the stable disease-free state). This transient tracking of the unstable disease-free state when predicts regime shifts that cause the delayed disease outbreak in a changing environment. Furthermore, the disease can disappear in advance (or belatedly) if the rate of environmental change is negative and large (or small). The transient dynamics of an infectious disease heavily depend on the initial infection number and rate or the speed of environmental change. Supplementary Information The online version contains supplementary material available at 10.1007/s00285-022-01787-3.

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Section: Introductionmentioning

confidence: 99%

An SIRS model with nonmonotone incidence and saturated treatment in a changing environment

2022

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“…ere is no central server in the public chain, which is completely decentralized, allowing everyone to participate in maintenance. Users can freely enter and exit the blockchain network, publicly send transactions and participate in consensus, but the transaction efficiency is low [12]. e public chain is applicable to digital currency, finance, and other scenarios.…”

Section: Blockchain Classificationmentioning

confidence: 99%

Research and Practice Analysis of Higher Vocational Colleges Facing the Experience and Dissemination of Regional Characteristic Tea Culture

Yan

2022

Advances in Multimedia

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Tea culture has special relevance in China’s cultural system. It is closely related to the development of tea industry. It is also an important branch of China’s traditional cultural system. Therefore, it must be paid great attention to. Especially in the context of big data, computer technology is widely used in the links of culture or information communication, and its purpose is to improve the communication effect. Therefore, the dissemination of tea culture information can be realized with the help of computer technology. From this perspective, this paper analyzes the development of computer technology in the background of big data, summarizes the necessity of using computer technology in the dissemination of tea culture information and, on this basis, considers the application strategy of computer technology in the dissemination of tea culture information from the perspective of big data, hoping to enter a more ideal pattern of tea culture information dissemination.

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Complexity of Government response to COVID-19 pandemic: a perspective of coupled dynamics on information heterogeneity and epidemic outbreak

Zhang

Shu

et al. 2023

Nonlinear Dyn

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Qualitative analysis and optimal control of an SIR model with logistic growth, non-monotonic incidence and saturated treatment

Cited by 12 publications

References 27 publications

An SIRS model with nonmonotone incidence and saturated treatment in a changing environment

An SIRS model with nonmonotone incidence and saturated treatment in a changing environment

Research and Practice Analysis of Higher Vocational Colleges Facing the Experience and Dissemination of Regional Characteristic Tea Culture

Complexity of Government response to COVID-19 pandemic: a perspective of coupled dynamics on information heterogeneity and epidemic outbreak

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