Global Hopf bifurcation analysis of an susceptible-infective-removed epidemic model incorporating media coverage with time delay

Zhao, Huitao; Zhao, Ming

doi:10.1080/17513758.2016.1229050

Cited by 16 publications

(5 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The detailed biological meanings of variables and parameters in systems (1) and ( 2) are listed in Table 1. The values of most parameters in Table 1 are derived from references [12,15,27]. In order to adapt to the new models, this article has made appropriate modifications to the values of parameters d 1 and d within a reasonable range based on [15].…”

Section: Models Formulationmentioning

confidence: 99%

See 1 more Smart Citation

Dynamic Analysis and Optimal Control of Fractional Order African Swine Fever Models with Media Coverage

Shi

Zhang

Wang

2023

Animals

View full text Add to dashboard Cite

African swine fever is a highly contagious virus that causes pig disease. Its onset process is short, but the mortality rate is as high as 100%. There are still no effective drugs that have been developed to treat African swine fever, and prevention and control measures are currently the best means to avoid infection in pig herds. In this paper, two fractional order mathematical models with media coverage are constructed to describe the transmission of African swine fever. The first model is a basic model with media coverage, and no control measures are considered. For this model, the reproduction number is obtained by using the next generation matrix method. Then, the sufficient conditions for the existence and stability of two equilibriums are obtained. Based on the first model, the second model is established incorporating two control measures. By using Pontryagin’s maximal principle, the optimal control solution is derived. After that, some numerical simulations are performed for the two models to verify the theoretical results. Both the qualitative analysis and numerical results indicate that timely media coverage combined with disinfection control measures is crucial to preventing the spread of disease.

show abstract

Section: Models Formulationmentioning

confidence: 99%

“…In [25,26], the authors proposed mathematical models, including nonlinear function as the transmission rate, and they studied the influence of media coverage on infectious diseases. In 2017, Zhao et al considered an SIR epidemic model combining time delay and media coverage [27].…”

Section: Introductionmentioning

confidence: 99%

Dynamic Analysis and Optimal Control of Fractional Order African Swine Fever Models with Media Coverage

Shi

Zhang

Wang

2023

Animals

View full text Add to dashboard Cite

show abstract

“…Among the mathematical tools currently used, delay differential models with time delay have attracted attention in the field of science especially modeling infectious diseases. Delays change the dynamical systems' stability by giving rise to Hopf-bifurcations [19,22]. Works done by researchers, for example, [8,[23][24][25][26], demonstrate the role played by time delays in different capacities in controlling the spread of infectious diseases.…”

Section: Introductionmentioning

confidence: 99%

Hopf-Bifurcation Analysis of Pneumococcal Pneumonia with Time Delays

Mbabazi¹,

Mugisha

Kimathi

2019

Abstract and Applied Analysis

View full text Add to dashboard Cite

In this paper, a mathematical model of pneumococcal pneumonia with time delays is proposed. The stability theory of delay differential equations is used to analyze the model. The results show that the disease-free equilibrium is asymptotically stable if the control reproduction ratioR0is less than unity and unstable otherwise. The stability of equilibria with delays shows that the endemic equilibrium is locally stable without delays and stable if the delays are under conditions. The existence of Hopf-bifurcation is investigated and transversality conditions are proved. The model results suggest that, as the respective delays exceed some critical value past the endemic equilibrium, the system loses stability through the process of local birth or death of oscillations. Further, a decrease or an increase in the delays leads to asymptotic stability or instability of the endemic equilibrium, respectively. The analytical results are supported by numerical simulations.

show abstract

“…Jiang et al constructed a S E I R S system with two delays, an explicit algorithm for determining the direction of Hopf bifurcations and the stability of the bifurcating periodic solutions were used by the center manifold and the normal form theory. Zhao and Zhao proposed a S I R epidemic model, incorporating media coverage with time delay, and showed that the local Hopf bifurcation implies the global Hopf bifurcation after the second critical value of delay. Moreover, the time delay affects the stability of the endemic equilibrium and produces limit cycle oscillations, whereas the basic reproduction number is greater than unity.…”

Section: Introductionmentioning

confidence: 99%

Cholera model incorporating media coverage with multiple delays

Shu

Yang

2018

Math Methods in App Sciences

View full text Add to dashboard Cite

In order to investigate the impact of awareness programs and time delays on the cholera outbreaks, we propose a cholera epidemic model, incorporating awareness programs by media as a separate class and two time‐delay factors. The bifurcation theory is applied to explore the variety of dynamics of this model for various combinations of the delays when R0>1. Moreover, we analyze the direction, stability, and period of the bifurcating periodic solutions arising through Hopf bifurcation by using the normal form concept and the center manifold theory. Finally, we present numerical simulations to verify the main theoretical results.

show abstract

Global Hopf bifurcation analysis of an susceptible-infective-removed epidemic model incorporating media coverage with time delay

Cited by 16 publications

References 28 publications

Dynamic Analysis and Optimal Control of Fractional Order African Swine Fever Models with Media Coverage

Dynamic Analysis and Optimal Control of Fractional Order African Swine Fever Models with Media Coverage

Hopf-Bifurcation Analysis of Pneumococcal Pneumonia with Time Delays

Cholera model incorporating media coverage with multiple delays

Contact Info

Product

Resources

About