Li-Martín Alian, Reyes-Carreto Ramón, Vargas-De-León Cruz
Facultad de Matemáticas, Universidad Autónoma de Guerrero, Ciudad Universitaria s/n Chilpancingo, Guerrero, México.
División de Investigación, Hospital Juárez de México, Ciudad de México, México.
Math Biosci Eng. 2023 Jan;20(1):955-974. doi: 10.3934/mbe.2023044. Epub 2022 Oct 20.
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.
年龄作为一个风险因素在媒介传播的传染病中很常见。部分原因是儿童依赖成年人采取预防措施，而且成年人比儿童更不易被蚊子叮咬，因为他们通常在户外的时间比儿童少。我们提出了一个登革热疾病模型，该模型将人群分为两个亚群：儿童和成年人。这样做是为了考虑到儿童比成年人更容易被蚊子叮咬。我们使用下一代算子方法计算了登革热的基本再生数。我们确定了无病平衡点的局部和全局稳定性。我们使用李雅普诺夫泛函方法获得了地方病平衡点全局渐近稳定性的充分条件。当儿童和成年人的感染期相同时，我们发现当阈值量(R_0 > 1)时，地方病平衡点在可行区域内部是全局渐近稳定的。此外，我们使用从文献中获得的参数值进行了数值模拟。最后，进行了局部敏感性分析，以确定对((R_0))变化影响最大的参数，从而对结果有更好的生物学解释。
