Analysis and Bayesian estimation of a model for Chikungunya dynamics with relapse: An outbreak in Acapulco, Mexico

María Guadalupe Vázquez-Peña; Cruz Vargas-De-León; Jorge Fernando Camacho-Pérez; Jorge Velázquez-Castro; María Guadalupe Vázquez-Peña; Cruz Vargas-De-León; Jorge Fernando Camacho-Pérez; Jorge Velázquez-Castro

doi:10.3934/mbe.2023805

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 10: 18123-18145. doi: 10.3934/mbe.2023805

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Research article Special Issues

Analysis and Bayesian estimation of a model for Chikungunya dynamics with relapse: An outbreak in Acapulco, Mexico

1.
Facultad de Ciencias Físico-Matemáticas, Benemérita Universidad Autónoma de Puebla, Puebla, México
2.
División de Investigación, Hospital Juárez de México, Ciudad de México 07760, México
3.
Sección de Estudios de Posgrado e Investigación, Escuela Superior de Medicina, Instituto Politécnico Nacional, Ciudad de México 11340, México
4.
Maestría en Ciencias de la Complejidad, Universidad Autónoma de la Ciudad de México, 03100 CDMX, México

Received: 24 July 2023 Revised: 03 September 2023 Accepted: 06 September 2023 Published: 21 September 2023

Chikungunya is a vector-borne viral disease transmitted by Aedes aegypti and Aedes albopictus mosquitoes. It does not have any specific treatment, and there is no vaccine. Recent epidemiological data have indicated that a relapse of the infection can occur within three months of the initial infection; however, until now, mathematical models for the spread of the disease have not considered this factor. We propose a mathematical model for the transmission of the Chikungunya virus that considers relapse. We calculated the basic reproductive number $ (R_0) $ of the disease by using the next-generation operator method. We proved the existence of a forward bifurcation. We determined the existence and the global stability of the equilibrium points by using the Lyapunov function method. We fitted the model to data from an outbreak in 2015 in Acapulco, Mexico to estimate the model parameters and $ R_0 $ with the Bayesian approach via a Hamiltonian Monte Carlo method. In the local sensitivity analysis, we found that the fraction of infected individuals who become asymptomatic has a strong impact on the basic reproductive number and makes some control measures insufficient. The impact of the fraction of infected individuals who become asymptomatic should be considered in Chikungunya control strategies.
- Chikungunya virus outbreaks,
- bifurcation analysis,
- direct Lyapunov method,
- Bayesian estimation,
- local sensitivity analysis
Citation: María Guadalupe Vázquez-Peña, Cruz Vargas-De-León, Jorge Fernando Camacho-Pérez, Jorge Velázquez-Castro. Analysis and Bayesian estimation of a model for Chikungunya dynamics with relapse: An outbreak in Acapulco, Mexico[J]. Mathematical Biosciences and Engineering, 2023, 20(10): 18123-18145. doi: 10.3934/mbe.2023805

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Abstract

Chikungunya is a vector-borne viral disease transmitted by Aedes aegypti and Aedes albopictus mosquitoes. It does not have any specific treatment, and there is no vaccine. Recent epidemiological data have indicated that a relapse of the infection can occur within three months of the initial infection; however, until now, mathematical models for the spread of the disease have not considered this factor. We propose a mathematical model for the transmission of the Chikungunya virus that considers relapse. We calculated the basic reproductive number $ (R_0) $ of the disease by using the next-generation operator method. We proved the existence of a forward bifurcation. We determined the existence and the global stability of the equilibrium points by using the Lyapunov function method. We fitted the model to data from an outbreak in 2015 in Acapulco, Mexico to estimate the model parameters and $ R_0 $ with the Bayesian approach via a Hamiltonian Monte Carlo method. In the local sensitivity analysis, we found that the fraction of infected individuals who become asymptomatic has a strong impact on the basic reproductive number and makes some control measures insufficient. The impact of the fraction of infected individuals who become asymptomatic should be considered in Chikungunya control strategies.

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