Analysis of a reaction-diffusion AIDS model with media coverage and population heterogeneity

Xiang Zhang; Tingting Zheng; Yantao Luo; Pengfei Liu; Xiang Zhang; Tingting Zheng; Yantao Luo; Pengfei Liu

doi:10.3934/era.2025024

Electronic Research Archive

2025, Volume 33, Issue 1: 513-536. doi: 10.3934/era.2025024

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Research article

Analysis of a reaction-diffusion AIDS model with media coverage and population heterogeneity

1.
College of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, China
2.
College of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830017, China
3.
Xinjiang Key Laboratory of Applied Mathematics, Urumqi 830017, China
4.
College of Mathematical Sciences, Shanxi University, Taiyuan 030006, China

Received: 20 November 2024 Revised: 13 January 2025 Accepted: 22 January 2025 Published: 24 January 2025

Considering the influence of population heterogeneity, media coverage and spatial diffusion on disease transmission, this paper investigated an acquired immunodeficiency syndrome (AIDS) reaction-diffusion model with nonlinear incidence rates and media coverage. First, we discussed the positivity and boundedness of system solutions. Then, the basic reproduction number $ \mathcal{R}_0 $ was calculated, and the disease-free equilibrium (DFE), denoted as $ E^0 $, was locally and globally asymptotically stable when $ \mathcal{R}_0 < 1 $. Further, there existed a unique endemic equilibrium (EE), denoted as $ E^* $, which was locally and globally asymptotically stable when $ \mathcal{R}_0 > 1 $ and certain additional conditions were satisfied. In addition, we showed that the disease was uniformly persistent. Finally, the visualization results of the numerical simulations illustrated that: The media coverage was shown to mitigate the AIDS transmission burden in the population by lowering the infection peak and the time required to reach it; a higher awareness conversion rate can effectively reduce the basic reproduction number $ \mathcal{R}_0 $ to curb the spread of AIDS.
- AIDS model,
- reaction-diffusion,
- media coverage,
- population heterogeneity,
- awareness conversion
Citation: Xiang Zhang, Tingting Zheng, Yantao Luo, Pengfei Liu. Analysis of a reaction-diffusion AIDS model with media coverage and population heterogeneity[J]. Electronic Research Archive, 2025, 33(1): 513-536. doi: 10.3934/era.2025024

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Abstract

Considering the influence of population heterogeneity, media coverage and spatial diffusion on disease transmission, this paper investigated an acquired immunodeficiency syndrome (AIDS) reaction-diffusion model with nonlinear incidence rates and media coverage. First, we discussed the positivity and boundedness of system solutions. Then, the basic reproduction number $ \mathcal{R}_0 $ was calculated, and the disease-free equilibrium (DFE), denoted as $ E^0 $, was locally and globally asymptotically stable when $ \mathcal{R}_0 < 1 $. Further, there existed a unique endemic equilibrium (EE), denoted as $ E^* $, which was locally and globally asymptotically stable when $ \mathcal{R}_0 > 1 $ and certain additional conditions were satisfied. In addition, we showed that the disease was uniformly persistent. Finally, the visualization results of the numerical simulations illustrated that: The media coverage was shown to mitigate the AIDS transmission burden in the population by lowering the infection peak and the time required to reach it; a higher awareness conversion rate can effectively reduce the basic reproduction number $ \mathcal{R}_0 $ to curb the spread of AIDS.

References

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