Threshold Dynamics and Probability Density Function of a Stochastic Avian Influenza Epidemic Model with Nonlinear Incidence Rate and Psychological Effect

Zhou, Baoquan; Jiang, Daqing; Dai, Yucong; Hayat, Tasawar

doi:10.1007/s00332-022-09885-8

Cited by 32 publications

(6 citation statements)

References 31 publications

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“…But, urban public health emergencies are second only to natural disasters in terms of casualties, and disaster prevention and control facilities for public health events such as urban epidemics are critical to sustainable urban development and urban safety ( 79 ). In addition to the number and spatial distribution of epidemic prevention facilities, the capacity and resilience of that also have a significant impact on epidemic prevention and control ( 12 , 80 ). Drawing on the international experience of dealing with natural disasters from disaster-prone countries, these issues ought to be fully considered in urban planning and incorporated into mandatory regulations in order to improve urban epidemic prevention laws and regulations.…”

Section: Discussionmentioning

confidence: 99%

Are the epidemic prevention facilities effective? How cities should choose epidemic prevention facilities: Taking Wuhan as an example

Hua

Ran

2023

Front. Public Health

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The COVID-19 pandemic highlighted the limitations of urban public health emergency response capabilities. Taking Wuhan as an example, this study used breakpoint regression, kernel density analysis, overlay analysis, and accessibility analysis from Stata and ArcGIS, and divided epidemic prevention facilities into the basic epidemic prevention facilities (hospitals), and the emergency epidemic prevention facilities (mobile cabin hospitals) for further analysis. The results showed that over 70% of the basic epidemic prevention facilities in Wuhan were located in high density population areas. On the contrary, most of the emergency epidemic prevention facilities were located in low density population areas. The local treatment effect of the implementation of the emergency epidemic prevention facility policy is about 1, indicating that there was a significant impact of emergency epidemic prevention facilities on outbreak control, which passed the bandwidth test. What’s more, the analysis of the accessibility of residential points revealed that more than 67.3% of people from the residential points could arrive at the epidemic prevention facilities within 15 min, and only 0.1% of them took more than 20 min to arrive. Therefore, the epidemic prevention facilities can effectively curb the spread of the epidemic, and people from residential areas can quickly get there. This study summarized the spatial characteristics of epidemic prevention facilities in Wuhan and analyzed the importance of them, thus providing a new perspective for future research on upgrading the city’s comprehensive disaster prevention system.

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Section: Discussionmentioning

confidence: 99%

Are the epidemic prevention facilities effective? How cities should choose epidemic prevention facilities: Taking Wuhan as an example

Hua

Ran

2023

Front. Public Health

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“…Lemma 2.2. ( [16]). For all real symmetric matrices A = (a ij ) 5×5 and Λ = diag{σ 1 , σ 2 , σ 3 , σ 4 , σ 5 },…”

Section: Basic Conceptsmentioning

confidence: 99%

A stochastic SIHR epidemic model with general population-size dependent contact rate and Ornstein–Uhlenbeck process: dynamics analysis

Mu,

Jiang

2024

Nonlinear Dyn

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The purpose of this work is to investigate a novel stochastic SIHR epidemic model, which includes a general incidence rate and mean-reversion Ornstein-Uhlenbeck process. Firstly, the existence of global positivity of the solution is testified by Lyapunov function. Secondly, this disease will be eradicated if R s 0 < 1. Otherwise, if R * 0 > 1, then the system has a stationary distribution, which means that the pandemic will persist. In addition, an explicit expression of the probability density function for a linear system near quasi-endemic equilibrium is obtained under certain conditions.Finally, a series of numerical simulations are carried out to validate the theoretical conclusions.

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“…[4][5][6] In the landscape of infectious disease modeling, the incorporation of environmental noise, particularly in the study of diseases such as measles, assumes paramount importance. [7][8][9] Environmental noise introduces a stochastic dimension that reflects the inherent unpredictability observed in real-world epidemiological systems. The exploration of infectious disease dynamics under the influence of environmental noise provides a nuanced understanding of the intricate interplay between stochastic factors and disease transmission dynamics.…”

Section: Introductionmentioning

confidence: 99%

“…In the landscape of infectious disease modeling, the incorporation of environmental noise, particularly in the study of diseases such as measles, assumes paramount importance 7–9 . Environmental noise introduces a stochastic dimension that reflects the inherent unpredictability observed in real‐world epidemiological systems.…”

Section: Introductionmentioning

confidence: 99%

Unveiling measles transmission dynamics: Insights from a stochastic model with nonlinear incidence

Shi,

Jiang

2024

Stud Appl Math

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In this paper, taking into account the inevitable impact of environmental perturbations on disease transmission, we primarily investigate a stochastic model for measles infection with nonlinear incidence. The transmission rate in this model follows a logarithmic normal distribution influenced by an Ornstein–Uhlenbeck (OU) process. To analyze the dynamic properties of the stochastic model, our first step is to establish the existence and uniqueness of a global solution for the stochastic equations. Next, by constructing appropriate Lyapunov functions and utilizing the ergodicity of the OU process, we establish sufficient conditions for the existence of a stationary distribution, indicating the prevalence of the disease. Furthermore, we provide sufficient conditions for disease elimination. These conditions are derived by considering the interplay between the model parameters and the stochastic dynamics. Finally, we validate the theoretical conclusions through numerical simulations, which allow us to assess the practical implications of the established conditions and observe the dynamics of the stochastic model in action. By combining theoretical analysis and numerical simulations, we gain a comprehensive understanding of the stochastic model's behavior, contributing to the broader understanding of measles transmission dynamics and the development of effective control strategies.

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Threshold Dynamics and Probability Density Function of a Stochastic Avian Influenza Epidemic Model with Nonlinear Incidence Rate and Psychological Effect

Cited by 32 publications

References 31 publications

Are the epidemic prevention facilities effective? How cities should choose epidemic prevention facilities: Taking Wuhan as an example

Are the epidemic prevention facilities effective? How cities should choose epidemic prevention facilities: Taking Wuhan as an example

A stochastic SIHR epidemic model with general population-size dependent contact rate and Ornstein–Uhlenbeck process: dynamics analysis

Unveiling measles transmission dynamics: Insights from a stochastic model with nonlinear incidence

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