We analyse the time-series evolution of the cumulative number of confirmed cases of COVID-19, the novel coronavirus disease, for some African countries. We propose a mathematical model, incorporating non-pharmaceutical interventions to unravel the disease transmission dynamics. Analysis of the stability of the model’s steady states was carried out, and the reproduction number ${\mathcal{R}}_0$, a vital key for flattening the time-evolution of COVID-19 cases, was obtained by means of the next generation matrix technique. By dividing the time evolution of the pandemic for the cumulative number of confirmed infected cases into different regimes or intervals, hereafter referred to as phases, numerical simulations were performed to fit the proposed model to the cumulative number of confirmed infections for different phases of COVID-19 during its first wave. The estimated ${\mathcal{R}}_0$ declined from 2.452–9.179 during the first phase of the infection to 1.374–2.417 in the last phase. Using the Atangana–Baleanu fractional derivative, a fractional COVID-19 model is proposed and numerical simulations performed to establish the dependence of the disease dynamics on the order of the fractional derivatives. An elasticity and sensitivity analysis of ${\mathcal{R}}_0$ was carried out to determine the most significant parameters for combating the disease outbreak. These were found to be the effective disease transmission rate, the disease diagnosis or case detection rate, the proportion of susceptible individuals taking precautions, and the disease infection rate. Our results show that if the disease infection rate is less than 0.082/day, then ${\mathcal{R}}_0$ is always less than 1; and if at least 55.29% of the susceptible population take precautions such as regular hand washing with soap, use of sanitizers, and the wearing of face masks, then the reproduction number ${\mathcal{R}}_0$ remains below unity irrespective of the disease infection rate. Keeping ${\mathcal{R}}_0$ values below unity leads to a decrease in COVID-19 prevalence.

我们分析了一些非洲国家 COVID-19（新型冠状病毒病）确诊病例累计数量的时间序列演变。我们提出了一个数学模型，结合非药物干预来揭示疾病传播动力学。对模型稳态的稳定性进行了分析，再现数${\mathcal{R}}_0$，通过下一代矩阵技术获得了扁平化 COVID-19 病例时间演变的重要关键。通过将大流行病的累计确诊感染病例数的时间演变划分为不同的制度或间隔，以下简称阶段，进行数值模拟，使所提出的模型与 COVID-19 不同阶段的累计确诊感染数相匹配19 在第一波期间。估计的${\mathcal{R}}_0$从感染第一阶段的 2.452-9.179 下降到最后阶段的 1.374-2.417。使用 Atangana–Baleanu 分数阶导数，提出了一个分数阶 COVID-19 模型，并进行了数值模拟以建立疾病动力学对分数阶导数阶数的依赖性。的弹性和敏感性分析${\mathcal{R}}_0$进行了确定对抗疾病爆发的最重要参数。发现这些是疾病有效传播率、疾病诊断或病例检出率、采取预防措施的易感人群比例和疾病感染率。我们的结果表明，如果疾病感染率小于 0.082/天，则${\mathcal{R}}_0$总是小于 1；如果至少 55.29% 的易感人群采取了预防措施，例如定期用肥皂洗手、使用消毒剂和戴口罩，那么再生产数${\mathcal{R}}_0$无论疾病感染率如何，都低于统一值。保持${\mathcal{R}}_0$低于统一的值会导致 COVID-19 流行率下降。