Global stability for a mosquito-borne disease model with continuous-time age structure in the susceptible and relapsed host classes

Maria Guadalupe Vazquez-Peña; Cruz Vargas-De-León; Jorge Velázquez-Castro; Maria Guadalupe Vazquez-Peña; Cruz Vargas-De-León; Jorge Velázquez-Castro

doi:10.3934/mbe.2024333

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 11: 7582-7600. doi: 10.3934/mbe.2024333

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Global stability for a mosquito-borne disease model with continuous-time age structure in the susceptible and relapsed host classes

1.
Centro de Investigación en Matemáticas, 36023 Guanajuato, Guanajuato, Mexico
2.
División de Investigación, Hospital Juárez de México, Ciudad de México 07760, Mexico
3.
Sección de Estudios de Posgrado e Investigación, Escuela Superior de Medicina, Instituto Politécnico Nacional, Ciudad de México 11340, Mexico
4.
Facultad de Ciencias Físico-Matemáticas, Benemérita Universidad Autónoma de Puebla, Puebla, Mexico

Academic Editor: Mingji Zhang

Received: 29 August 2024 Revised: 28 October 2024 Accepted: 06 November 2024 Published: 14 November 2024

Mosquito-borne infectious diseases represent a significant public health issue. Age has been identified as a key risk factor for these diseases, and another phenomenon reported is relapse, which involves the reappearance of symptoms after a symptom-free period. Recent research indicates that susceptibility to and relapse of mosquito-borne diseases are frequently age-dependent. This paper proposes a new model to better capture the dynamics of mosquito-borne diseases by integrating two age-dependent factors: chronological age and asymptomatic-infection age. Chronological age refers to the time elapsed from the date of birth of the host to the present time. On the other hand, asymptomatic infection age denotes the time elapsed since the host became asymptomatic after the primary infection. The system of integro-differential equations uses flexible, unspecified functions to represent these dependencies, assuming they are integrable. We analyzed the global stability of both the disease-free and endemic equilibrium states using the direct Lyapunov method with Volterra-type Lyapunov functionals. Additionally, the paper explores several special cases involving well-known host-vector models.
- mosquito-borne infectious diseases,
- age dependency,
- susceptibility,
- relapse,
- Volterra-type Lyapunov functions
Citation: Maria Guadalupe Vazquez-Peña, Cruz Vargas-De-León, Jorge Velázquez-Castro. Global stability for a mosquito-borne disease model with continuous-time age structure in the susceptible and relapsed host classes[J]. Mathematical Biosciences and Engineering, 2024, 21(11): 7582-7600. doi: 10.3934/mbe.2024333

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Abstract

Mosquito-borne infectious diseases represent a significant public health issue. Age has been identified as a key risk factor for these diseases, and another phenomenon reported is relapse, which involves the reappearance of symptoms after a symptom-free period. Recent research indicates that susceptibility to and relapse of mosquito-borne diseases are frequently age-dependent. This paper proposes a new model to better capture the dynamics of mosquito-borne diseases by integrating two age-dependent factors: chronological age and asymptomatic-infection age. Chronological age refers to the time elapsed from the date of birth of the host to the present time. On the other hand, asymptomatic infection age denotes the time elapsed since the host became asymptomatic after the primary infection. The system of integro-differential equations uses flexible, unspecified functions to represent these dependencies, assuming they are integrable. We analyzed the global stability of both the disease-free and endemic equilibrium states using the direct Lyapunov method with Volterra-type Lyapunov functionals. Additionally, the paper explores several special cases involving well-known host-vector models.

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