Department of Mathematics, Muslim University of Morogoro, Morogoro, Tanzania.
Department of Mathematics and Statistics, University of Dodoma, Dodoma, Tanzania.
J Biol Dyn. 2020 Dec;14(1):748-766. doi: 10.1080/17513758.2020.1823494.
The outbreak of COVID-19 was first experienced in Wuhan City, China, during December 2019 before it rapidly spread over globally. This paper has proposed a mathematical model for studying its transmission dynamics in the presence of face mask wearing and hospitalization services of human population in Tanzania. Disease-free and endemic equilibria were determined and subsequently their local and global stabilities were carried out. The trace-determinant approach was used in the local stability of disease-free equilibrium point while Lyapunov function technique was used to determine the global stability of both disease-free and endemic equilibrium points. Basic reproduction number, , was determined in which its numerical results revealed that, in the presence of face masks wearing and medication services or hospitalization as preventive measure for its transmission, while in their absence . This supports its analytical solution that the disease-free equilibrium point is asymptotically stable whenever , while endemic equilibrium point is globally asymptotically stable for . Therefore, this paper proves the necessity of face masks wearing and hospitalization services to COVID-19 patients to contain the disease spread to the population.
COVID-19 的爆发首先在中国武汉市经历，然后迅速在全球范围内传播。本文提出了一个数学模型，用于研究坦桑尼亚人口在戴口罩和住院治疗服务情况下的传播动力学。确定了无病平衡点和地方平衡点，并对其局部和全局稳定性进行了分析。利用迹-决定方法研究无病平衡点的局部稳定性，利用李雅普诺夫函数技术确定无病平衡点和地方平衡点的全局稳定性。基本再生数 ，数值结果表明，在戴口罩和药物治疗或住院治疗等预防措施的情况下， ，而在没有这些措施的情况下， 。这支持了其解析解，即当 ，无病平衡点 是渐近稳定的，而在 ，地方平衡点 是全局渐近稳定的。因此，本文证明了戴口罩和对 COVID-19 患者进行住院治疗是控制疾病在人群中传播的必要性。
