Age as a risk factor is common in vector-borne infectious diseases. This is partly because children depend on adults to take preventative measures, and adults are less susceptible to mosquito bites because they generally spend less time outdoors than children. We propose a dengue disease model that considers the human population as divided into two subpopulations: children and adults. This is in order to take into consideration that children are more likely than adults to be bitten by mosquitoes. We calculated the basic reproductive number of dengue, using the next-generation operator method. We determined the local and global stability of the disease-free equilibrium. We obtained sufficient conditions for the global asymptotic stability of the endemic equilibrium using the Lyapunov functional method. When the infected periods in children and adults are the same, we that the endemic equilibrium is globally asymptotically stable in the interior of the feasible region when the threshold quantity $ R_0 > 1 $. Additionally, we performed a numerical simulation using parameter values obtained from the literature. Finally, a local sensitivity analysis was performed to identify the parameters that have the greatest influence on changes in $ (R_0) $, and thereby obtain a better biological interpretation of the results.
Citation: Alian Li-Martín, Ramón Reyes-Carreto, Cruz Vargas-De-León. Dynamics of a dengue disease transmission model with two-stage structure in the human population[J]. Mathematical Biosciences and Engineering, 2023, 20(1): 955-974. doi: 10.3934/mbe.2023044
Age as a risk factor is common in vector-borne infectious diseases. This is partly because children depend on adults to take preventative measures, and adults are less susceptible to mosquito bites because they generally spend less time outdoors than children. We propose a dengue disease model that considers the human population as divided into two subpopulations: children and adults. This is in order to take into consideration that children are more likely than adults to be bitten by mosquitoes. We calculated the basic reproductive number of dengue, using the next-generation operator method. We determined the local and global stability of the disease-free equilibrium. We obtained sufficient conditions for the global asymptotic stability of the endemic equilibrium using the Lyapunov functional method. When the infected periods in children and adults are the same, we that the endemic equilibrium is globally asymptotically stable in the interior of the feasible region when the threshold quantity $ R_0 > 1 $. Additionally, we performed a numerical simulation using parameter values obtained from the literature. Finally, a local sensitivity analysis was performed to identify the parameters that have the greatest influence on changes in $ (R_0) $, and thereby obtain a better biological interpretation of the results.
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Alian Li-Martín, Ramón Reyes-Carreto, Cruz Vargas-De-León. Dynamics of a dengue disease transmission model with two-stage structure in the human population[J]. Mathematical Biosciences and Engineering, 2023, 20(1): 955-974. doi: 10.3934/mbe.2023044
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