Bifurcation Analysis of an Sirs Epidemic Model With Standard Incidence Rate and Saturated Treatment Function

Gao, Yixian; Zhang, Weipeng; Liú, Dan; Xiao, None Yanju

doi:10.11948/2017067

Cited by 4 publications

(3 citation statements)

References 43 publications

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“…This methodology biologically groups the compartmental model into two vectors which are denoted by and , and represent, respectively, the rate of appearance of new infections in compartment i and the remaining transitional terms (namely births, deaths, disease progression and recovery [ 12 , 27 ]?). Following [ 12 ], we readily obtain that and, as a consequence, . Moreover, the following system is obtained: For the remainder, let .…”

Section: Steady States and Linear Stability Analysismentioning

confidence: 99%

“…Classical epidemiological models are constantly improved to provide more realistic descriptions. For example, some of those systems consider nonlinear incidence rates in both transmission and treatment [ 12 , 13 ]. In particular, the Beddington–DeAngelis incidence rate is frequently used to take into account the limitations of disease spreading due to treatment and preventive measures [ 13 ].…”

Section: Introductionmentioning

confidence: 99%

“…In particular, the Beddington–DeAngelis incidence rate is frequently used to take into account the limitations of disease spreading due to treatment and preventive measures [ 13 ]. On the other hand, the Holling type II treatment is capable of accounting for the limitation access to treatment due to financial and economic costs, low test of infected during the disease spreading and unexpected effects of treatment [ 12 ]. The analysis of such systems is generally carried out using time series which forecast the epidemiological behavior at a giving time.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics of a cross-superdiffusive SIRS model with delay effects in transmission and treatment

et al. 2023

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We investigate the dynamics of a SIRS epidemiological model taking into account cross-superdiffusion and delays in transmission, Beddington–DeAngelis incidence rate and Holling type II treatment. The superdiffusion is induced by inter-country and inter-urban exchange. The linear stability analysis for the steady-state solutions is performed, and the basic reproductive number is calculated. The sensitivity analysis of the basic reproductive number is presented, and we show that some parameters strongly influence the dynamics of the system. A bifurcation analysis to determine the direction and stability of the model is carried out using the normal form and center manifold theorem. The results reveal a proportionality between the transmission delay and the diffusion rate. The numerical results show the formation of patterns in the model, and their epidemiological implications are discussed.

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Section: Steady States and Linear Stability Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamics of a cross-superdiffusive SIRS model with delay effects in transmission and treatment

et al. 2023

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Bifurcation analysis of a network-based SIR epidemic model with saturated treatment function

Yousef

2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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In this paper, we present a study on a network-based susceptible-infected-recovered (SIR) epidemic model with a saturated treatment function. It is well known that treatment can have a specific effect on the spread of epidemics, and due to the limited resources of treatment, the number of patients during severe disease outbreaks who need to be treated may exceed the treatment capacity. Consequently, the number of patients who receive treatment will reach a saturation level. Thus, we incorporated a saturated treatment function into the model to characterize such a phenomenon. The dynamics of the present model is discussed in this paper. We first obtained a threshold value R0, which determines the stability of a disease-free equilibrium. Furthermore, we investigated the bifurcation behavior at R0=1. More specifically, we derived a condition that determines the direction of bifurcation at R0=1. If the direction is backward, then a stable disease-free equilibrium concurrently exists with a stable endemic equilibrium even though R0<1. Therefore, in this case, R0<1 is not sufficient to eradicate the disease from the population. However, if the direction is forward, we find that for a range of parameters, multiple equilibria could exist to the left and right of R0=1. In this case, the initial infectious invasion must be controlled to a lower level so that the disease dies out or approaches a lower endemic steady state.

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Nonconstant positive steady states and pattern formation of a diffusive epidemic model

Gao

2022

Electron. J. Qual. Theory Differ. Equ.

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It is our purpose in this paper to make a detailed description for the structure of the set of the nonconstant steady states for the two-dimensional epidemic S-I model with diffusion incorporating demographic and epidemiological processes with zero-flux boundary conditions. We first study the conditions of diffusion-driven instability occurrence, which induces spatial inhomogeneous patterns. The results will extend to the derivative of prey's functional response with prey is positive. Moreover, we establish the local and global structure of nonconstant positive steady state solutions. A priori estimates for steady state solutions will play a key role in the proof. Our results indicate that the diffusion has a great influence on the spread of the epidemic and extend well the finding of spatiotemporal dynamics in the epidemic model.

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Bifurcation Analysis of an Sirs Epidemic Model With Standard Incidence Rate and Saturated Treatment Function

Cited by 4 publications

References 43 publications

Dynamics of a cross-superdiffusive SIRS model with delay effects in transmission and treatment

Dynamics of a cross-superdiffusive SIRS model with delay effects in transmission and treatment

Bifurcation analysis of a network-based SIR epidemic model with saturated treatment function

Nonconstant positive steady states and pattern formation of a diffusive epidemic model

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