We develop a mathematical model for the transmission and spread of infections caused by the severe acute respiratory syndrome coronavirus 2 (SAR-CoV-2) which causes the coronavirus disease 2019 (COVID-19), a disease that has since been classified, by the World Health Organization, as a global pandemic. We focus attention on virus transmissions in a closed population and hence use a compartmental epidemic model to study the inherent dynamics of infections between the various subgroups of the population. We assume random interactions between members from different subgroups and hence we employ stochastic modelling techniques. In the absence of a vaccine for this novel coronavirus, governments worldwide have put in place various intervention strategies, including travel bans, lockdowns, screening, testing, quarantine, etc. in order to reduce and hopefully eliminate the transmission and spread of the COVID-19 virus. These interventions are built into our model and we investigate their effects and effectiveness. In particular, we observe that the two subgroups containing infectious individuals, namely; the subgroup comprising of unidentified asymptomatic individuals as well as; the subgroup comprising of un-quarantined symptomatic individuals; pose the greatest risk of the transmission and spread of infections. We therefore also observe from our results that; rapid (realtime) mass testing as well as effective (or mandatory) quarantine of all infected individuals are the fundamentally critical and necessary steps in reducing the internal transmissions and spread of the COVID-19 virus. In particular, our results indicate that lockdowns are only important to the extent that, if implemented effectively, they help in reducing the rate of transmissions (i.e. help to ‘flatten’ the transmission curves) and hence allow policy makers and healthcare practitioners to put in place the important processes of realtime mass testing and mandatory quarantine, including hospitalization and treatment. Our results are presented over a single wave (or part of a single wave) of COVID-19 infections in a given population. If conditions are repeated, the results would correspondingly extend to multiple waves of infection.

我们开发了一个由严重急性呼吸综合征冠状病毒 2 (SAR-CoV-2) 引起的感染传播和传播的数学模型，这种病毒会导致 2019 年冠状病毒病 (COVID-19)，这种疾病后来被分类为世界卫生组织将其列为全球大流行病。我们将注意力集中在封闭人群中的病毒传播，因此使用区室流行病模型来研究人群各个亚组之间感染的内在动态。我们假设来自不同子组的成员之间存在随机交互，因此我们采用随机建模技术。在缺乏针对这种新型冠状病毒的疫苗的情况下，世界各国政府采取了各种干预策略，包括旅行禁令、封锁、筛查、检测、隔离等，以减少并有望消除新冠病毒的传播和蔓延。 19 病毒。这些干预措施已纳入我们的模型中，我们会研究它们的效果和有效性。特别是，我们观察到包含传染性个体的两个亚组，即：由身份不明的无症状个体组成的亚组；由未隔离的有症状个体组成的亚组；造成感染传播和蔓延的最大风险。因此，我们还从我们的结果中观察到：对所有感染者进行快速（实时）大规模检测以及有效（或强制）隔离是减少 COVID-19 病毒内部传播和传播的根本关键和必要步骤。特别是，我们的结果表明，封锁的重要性仅在于，如果有效实施，它们有助于降低传播率（即有助于“拉平”传播曲线），从而允许政策制定者和医疗保健从业者投入安排实时大规模检测和强制隔离的重要流程，包括住院和治疗。我们的结果是针对特定人群中的单波（或单波）COVID-19 感染的一部分得出的。如果情况重复，结果将相应地扩大到多波感染。