发表机构
Jordan University College（约旦大学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对流感-肺炎球菌共感染，构建十二仓室ODE模型，发现携带者传播超过退出率时发生后向分支，使降低基本再生数不足以消除，并通过全局敏感性分析揭示跨病原体协同作用。
AI 中文摘要
细菌共感染，尤其是与肺炎链球菌的共感染，是流感流行期间发病的主要驱动因素，且这一负担不成比例地落在撒哈拉以南非洲地区，在那里两种病原体全年以高水平循环，肺炎球菌携带在该地区普遍且持续存在。然而，现有的数学模型很少在宿主通过恢复的完整流感史的同时追踪其细菌携带状态。我们开发了一个十二仓室常微分方程模型，该模型根据病毒状态（易感、感染、恢复）和细菌状态（易感、携带者、活动性感染、恢复）对每个宿主进行分类，允许携带者到活动性的进展依赖于先前的流感暴露。我们建立了正性、有界性和正不变区域，然后推导出单一疾病的基本再生数$\mathcal{R}_0$和准地方病平衡点，以及入侵再生数$\mathbf{Inv}^{\mathbf{B}}$和$\mathbf{Inv}^{\mathbf{V}}$，它们量化了每种病原体在另一种病原体已经地方性流行的群体中入侵的能力。中心流形分析表明，当携带者传播超过携带者的总退出率$\beta_c>\kappa_S+\theta+\mu$时，细菌子系统和完全共存平衡点恰好发生后向分支，因此将$\mathcal{R}_0$降至1以下不足以消除，而病毒子系统向前分支。全局敏感性分析（拉丁超立方体采样与偏秩相关系数）表明，病毒和细菌阈值主要由大部分独立的参数控制，而细菌入侵潜力强烈受病毒传播和恢复的影响，给出了跨病原体协同作用的定量特征。
英文摘要
Bacterial co-infection, particularly with \emph{Streptococcus pneumoniae}, is a major driver of morbidity during influenza epidemics, and this burden falls disproportionately on sub-Saharan Africa, where both pathogens circulate year-round at high levels and pneumococcal carriage remains common and persistent across the region. Yet existing mathematical models rarely track a host's bacterial carriage status jointly with their full influenza history through recovery. We develop a twelve-compartment ODE model that classifies each host by viral status (susceptible, infected, recovered) and bacterial status (susceptible, carrier, actively infected, recovered), allowing carrier-to-active progression to depend on prior influenza exposure. We establish positivity, boundedness, and a positively invariant region, then derive the basic reproduction number $\mathcal{R}_0$ and quasi-endemic equilibria of a single disease, together with invasion reproduction numbers $\mathbf{Inv}^{\mathbf{B}}$ and $\mathbf{Inv}^{\mathbf{V}}$ quantifying each pathogen's ability to invade a population where the other is already endemic. Center-manifold analysis shows that the bacterial subsystem and the full coexistence equilibrium undergo a backward bifurcation precisely when carrier transmission exceeds the carrier's total exit rate, $β_c>κ_S+θ+μ$, so that reducing $\mathcal{R}_0$ below one is not sufficient for elimination, while the viral subsystem bifurcates forward. A global sensitivity analysis (Latin Hypercube Sampling with partial rank correlation coefficients) shows that the viral and bacterial thresholds are governed by largely separate parameters, while the bacterial invasion potential is strongly shaped by viral transmission and recovery, giving a quantitative signature of cross-pathogen synergy.
