Dynamic interaction between transmission, within-host dynamics and mosquito density

Mayra Núñez-López; Jocelyn A. Castro-Echeverría; Jorge X. Velasco-Hernández; Mayra Núñez-López; Jocelyn A. Castro-Echeverría; Jorge X. Velasco-Hernández

doi:10.3934/mbe.2025051

Mathematical Biosciences and Engineering

2025, Volume 22, Issue 6: 1364-1381. doi: 10.3934/mbe.2025051

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Dynamic interaction between transmission, within-host dynamics and mosquito density

1.
Department of Mathematics, ITAM Río Hondo 1, Ciudad de México 01080, México
2.
Instituto de Matemáticas, UNAM, Boulevard Juriquilla No. 3001, Juriquilla Querétaro 76230, México
3.
Tecnologico de Monterrey, School of Engineering and Science, Blvd. Enrique Mazón López 965, Hermosillo, Sonora 83000, México

Academic Editor: Mingji Zhang

Received: 31 January 2025 Revised: 10 April 2025 Accepted: 18 April 2025 Published: 28 April 2025

The central question in this paper is the character and role of the within-host and between-host interactions in vector-transmitted diseases compared to environmental-transmitted diseases. In vector-transmitted diseases, the environmental stage becomes the vector population. We link an epidemiological model for a vector-transmitted disease with a simple immunological process: the effective transmission rate from host to vector, modeled as a function of the infected cell level within the host, and a virus inoculation term that depends on the abundance of infected mosquitoes. We explore the role of infectivity (defined as the number of host target cells infected), recovery rate, and viral clearance rate in the coupled dynamics of these systems. As expected, the conditions for a disease outbreak require the average individual in the population to have an active (within-host) viral infection. However, the outbreak's nature, duration, and dynamic characteristics depend on the intensity of the within-host infection and the nature of the mosquito transmission capacity. Through the model, we establish inter-relations between the infectivity, host recovery rate, viral clearance rate, and different dynamic behavior patterns at the population level.
- dengue transmission,
- multiple time scales,
- within-host dynamics,
- between-host dynamics,
- reproduction number
Citation: Mayra Núñez-López, Jocelyn A. Castro-Echeverría, Jorge X. Velasco-Hernández. Dynamic interaction between transmission, within-host dynamics and mosquito density[J]. Mathematical Biosciences and Engineering, 2025, 22(6): 1364-1381. doi: 10.3934/mbe.2025051

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Abstract

The central question in this paper is the character and role of the within-host and between-host interactions in vector-transmitted diseases compared to environmental-transmitted diseases. In vector-transmitted diseases, the environmental stage becomes the vector population. We link an epidemiological model for a vector-transmitted disease with a simple immunological process: the effective transmission rate from host to vector, modeled as a function of the infected cell level within the host, and a virus inoculation term that depends on the abundance of infected mosquitoes. We explore the role of infectivity (defined as the number of host target cells infected), recovery rate, and viral clearance rate in the coupled dynamics of these systems. As expected, the conditions for a disease outbreak require the average individual in the population to have an active (within-host) viral infection. However, the outbreak's nature, duration, and dynamic characteristics depend on the intensity of the within-host infection and the nature of the mosquito transmission capacity. Through the model, we establish inter-relations between the infectivity, host recovery rate, viral clearance rate, and different dynamic behavior patterns at the population level.

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