Global dynamics of a diffusive SIR epidemic model with saturated incidence rate and discontinuous treatments

Cao, Qi; Liu, Yuying; Yang, Wensheng

doi:10.1007/s40435-022-00935-3

Cited by 2 publications

(1 citation statement)

References 26 publications

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“…1+γ u X C of complication of T2 diabetes to without complication in saturated form, where treatment effect is denoted by u [30,31]. Here b γ denotes the supply of medical resources per unit time and γ denotes the saturation constant related to treatment control.…”

Section: Model Formulationmentioning

confidence: 99%

Optimal control for the complication of Type 2 diabetes: the role of awareness programs by media and treatment

Mollah

Biswas

2022

Int. J. Dynam. Control

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T2 diabetes is a silent killer and serious public health issue across the world, though awareness of diabetes allows understanding of the causes and prevention of the disease. With this inspiration, we formulate a deterministic model by incorporating awareness and saturated treatment function of the T2 diabetes model to study the dynamics of the disease. We have carried out thoroughly analysis of the model system, including positivity of solutions, boundedness, equilibrium, and stability analysis. Again, we consider the deterministic model system as an optimal control problem by taking awareness (M) and treatment (u) as time-depended control parameters. The sufficient conditions for optimal control for T2 diabetes are obtained utilizing the Pontryagin's maximum principle in time-dependent controls to find optimal strategies for disease control. We intended to assess the efficacy and costs of several strategies to determine which is the best cost-effective strategy with the limited resources for treatment. The parameters incident rate (β), awareness coefficient ( p), media (M), and treatment (u) highly influence the dynamics of T2 diabetes. Numerical simulations suggest that both awareness and treatment controls have a significant impact on the optimal system and are economically feasible to reduce the prevalence of T2 diabetes.

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Section: Model Formulationmentioning

confidence: 99%

Optimal control for the complication of Type 2 diabetes: the role of awareness programs by media and treatment

Mollah

Biswas

2022

Int. J. Dynam. Control

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Exploring the complex dynamics of a diffusive epidemic model: Stability and bifurcation analysis

Acharya,

Kumar Upadhyay,

Mondal

2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The recent pandemic has highlighted the need to understand how we resist infections and their causes, which may differ from the ways we often think about treating epidemic diseases. The current study presents an improved version of the susceptible-infected-recovered (SIR) epidemic model, to better comprehend the community’s overall dynamics of diseases, involving numerous infectious agents. The model deals with a non-monotone incidence rate that exhibits psychological or inhibitory influence and a saturation treatment rate. It has been identified that depending on the measure of medical resources and the effectiveness of their supply, the model exposes both forward and backward bifurcations where two endemic equilibria coexist with infection-free equilibrium. The model also experiences local and global bifurcations of codimension two, including saddle-node, Hopf, and Bogdanov–Takens bifurcations. Additionally, the stability of equilibrium points is investigated. For a spatially extended SIR model system, we have shown that cross-diffusion allows S and I populations to coexist in a habitat. Also, the Turing instability requirements and Turing bifurcation regime are derived. The relationship between distinct role-playing model parameters and various pattern formations like spot and stripe patterns is validated by carrying out in-depth numerical simulations. The findings in the vicinity of the endemic equilibrium solution demonstrate the significance of positive and negative valued cross-diffusion coefficients in regulating the genesis of spatial patterns in susceptible as well as diseased individuals. The discussion of the findings of epidemiological ramifications concludes the manuscript.

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Global dynamics of a diffusive SIR epidemic model with saturated incidence rate and discontinuous treatments

Cited by 2 publications

References 26 publications

Optimal control for the complication of Type 2 diabetes: the role of awareness programs by media and treatment

Optimal control for the complication of Type 2 diabetes: the role of awareness programs by media and treatment

Exploring the complex dynamics of a diffusive epidemic model: Stability and bifurcation analysis

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