Calvo-Monge Jimmy, Sanchez Fabio, Calvo Juan Gabriel, Mena Dario
Escuela de Matemática, Universidad de Costa Rica, Ciudad Universitaria Rodrigo Facio, San José, 11501, Costa Rica.
Centro de Investigación en Matemática Pura y Aplicada, Universidad de Costa Rica, Ciudad Universitaria Rodrigo Facio, San José, 11501, Costa Rica.
Infect Dis Model. 2023 Jun 30;8(3):769-782. doi: 10.1016/j.idm.2023.06.004. eCollection 2023 Sep.
Throughout the progress of epidemic scenarios, individuals in different health classes are expected to have different average daily contact behavior. This contact heterogeneity has been studied in recent adaptive models and allows us to capture the inherent differences across health statuses better. Diseases with reinfection bring out more complex scenarios and offer an important application to consider contact disaggregation. Therefore, we developed a nonlinear differential equation model to explore the dynamics of relapse phenomena and contact differences across health statuses. Our incidence rate function is formulated, taking inspiration from recent adaptive algorithms. It incorporates contact behavior for individuals in each health class. We use constant contact rates at each health status for our analytical results and prove conditions for different forward-backward bifurcation scenarios. The relationship between the different contact rates heavily influences these conditions. Numerical examples highlight the effect of temporarily recovered individuals and initial conditions on infected population persistence.
在疫情发展的整个过程中，不同健康等级的个体预计会有不同的平均每日接触行为。这种接触异质性在最近的适应性模型中已有研究，它能让我们更好地捕捉不同健康状况之间的内在差异。具有再感染情况的疾病会带来更复杂的情形，并为考虑接触细分提供了一个重要应用。因此，我们开发了一个非线性微分方程模型，以探索复发现象的动态变化以及不同健康状况之间的接触差异。我们的发病率函数是根据最近的自适应算法制定的。它纳入了每个健康等级个体的接触行为。为了得到分析结果，我们在每个健康状况下使用恒定的接触率，并证明了不同的前后向分岔情形的条件。不同接触率之间的关系对这些条件有很大影响。数值例子突出了暂时康复个体和初始条件对感染人群持续存在的影响。
