The state of an infectious disease can represent the degree of infectivity of infected individuals, or susceptibility of susceptible individuals, or immunity of recovered individuals, or a combination of these measures. When the disease progression is long such as for HIV, individuals often experience switches among different states. We derive an epidemic model in which infected individuals have a discrete set of states of infectivity and can switch among different states. The model also incorporates a general incidence form in which new infections are distributed among different disease states. We discuss the importance of the transmission–transfer network for infectious diseases. Under the assumption that the transmission–transfer network is strongly connected, we establish that the basic reproduction number ${\mathcal{R}}_0$ is a sharp threshold parameter: if ${\mathcal{R}}_0\le 1$, the disease-free equilibrium is globally asymptotically stable and the disease always dies out; if ${\mathcal{R}}_0>1$, the disease-free equilibrium is unstable, the system is uniformly persistent and initial outbreaks lead to persistent disease infection. For a restricted class of incidence functions, we prove that there is a unique endemic equilibrium and it is globally asymptotically stable when ${\mathcal{R}}_0>1$. Furthermore, we discuss the impact of different state structures on ${\mathcal{R}}_0$, on the distribution of the disease states at the unique endemic equilibrium, and on disease control and preventions. Implications to the COVID-19 pandemic are also discussed.

传染病的状态可以代表受感染个体的传染性程度，或易感个体的易感性，或康复个体的免疫力，或这些措施的组合。当疾病进展较长时，例如艾滋病毒，个体经常会经历不同状态之间的切换。我们推导出一个流行病模型，其中受感染的个体具有一组离散的传染性状态，并且可以在不同状态之间切换。该模型还纳入了一般发病率形式，其中新感染分布在不同的疾病状态中。我们讨论了传染病传播网络的重要性。在传输-传递网络强连通的假设下，我们建立基本再生数${\mathcal{<span\; data-immersive-translate-walked="d23a6f41-177c-48e0-84dc-1536549bfe78">右</span>}}_{\mathrm{<span\; data-immersive-translate-walked="d23a6f41-177c-48e0-84dc-1536549bfe78">0</span>}}$是一个尖锐的阈值参数：如果${\mathcal{<span\; data-immersive-translate-walked="d23a6f41-177c-48e0-84dc-1536549bfe78">右</span>}}_{\mathrm{<span\; data-immersive-translate-walked="d23a6f41-177c-48e0-84dc-1536549bfe78">0</span>}}<span\; data-immersive-translate-walked="d23a6f41-177c-48e0-84dc-1536549bfe78">\le </span>\mathrm{<span\; data-immersive-translate-walked="d23a6f41-177c-48e0-84dc-1536549bfe78">1</span>}$ ，无病平衡是全局渐近稳定的，疾病总是会消失；如果${\mathcal{<span\; data-immersive-translate-walked="d23a6f41-177c-48e0-84dc-1536549bfe78">右</span>}}_{\mathrm{<span\; data-immersive-translate-walked="d23a6f41-177c-48e0-84dc-1536549bfe78">0</span>}}<span\; data-immersive-translate-walked="d23a6f41-177c-48e0-84dc-1536549bfe78">></span>\mathrm{<span\; data-immersive-translate-walked="d23a6f41-177c-48e0-84dc-1536549bfe78">1</span>}$ ，无病平衡不稳定，系统一致持续，最初的爆发导致持续的疾病感染。 对于一类受限的发生函数，我们证明存在独特的地方性平衡，并且当${\mathcal{<span\; data-immersive-translate-walked="d23a6f41-177c-48e0-84dc-1536549bfe78">右</span>}}_{\mathrm{<span\; data-immersive-translate-walked="d23a6f41-177c-48e0-84dc-1536549bfe78">0</span>}}<span\; data-immersive-translate-walked="d23a6f41-177c-48e0-84dc-1536549bfe78">></span>\mathrm{<span\; data-immersive-translate-walked="d23a6f41-177c-48e0-84dc-1536549bfe78">1</span>}$ 。此外，我们还讨论了不同国家结构对${\mathcal{<span\; data-immersive-translate-walked="d23a6f41-177c-48e0-84dc-1536549bfe78">右</span>}}_{\mathrm{<span\; data-immersive-translate-walked="d23a6f41-177c-48e0-84dc-1536549bfe78">0</span>}}$ ，关于疾病在独特的地方性平衡状态的分布，以及疾病的控制和预防。还讨论了对 COVID-19 大流行的影响。