a Department of Mathematics , University of Science and Technology , Bannu , Pakistan.
b Department of Mathematics , University of Malakand , Dir Lower , Pakistan.
J Biol Dyn. 2017 Dec;11(1):323-338. doi: 10.1080/17513758.2017.1339835.
This study proposes a mathematical model of Anthroponotic visceral leishmaniasis epidemic with saturated infection rate and recommends different control strategies to manage the spread of this disease in the community. To do this, first, a model formulation is presented to support these strategies, with quantifications of transmission and intervention parameters. To understand the nature of the initial transmission of the disease, the reproduction number [Formula: see text] is obtained by using the next-generation method. On the basis of sensitivity analysis of the reproduction number [Formula: see text], four different control strategies are proposed for managing disease transmission. For quantification of the prevalence period of the disease, a numerical simulation for each strategy is performed and a detailed summary is presented. Disease-free state is obtained with the help of control strategies. The threshold condition for globally asymptotic stability of the disease-free state is found, and it is ascertained that the state is globally stable. On the basis of sensitivity analysis of the reproduction number, it is shown that the disease can be eradicated by using the proposed strategies.
本研究提出了一个带有饱和感染率的人际内脏利什曼病的数学模型，并建议了不同的控制策略来管理该疾病在社区中的传播。为此，首先提出了一个模型公式来支持这些策略，对传播和干预参数进行量化。为了了解疾病初始传播的性质，通过使用下一代方法获得了繁殖数[公式：见文本]。基于繁殖数[公式：见文本]的敏感性分析，提出了四种不同的控制策略来管理疾病传播。对于每种策略的流行期的定量，都进行了数值模拟，并给出了详细的总结。借助控制策略获得了无病状态。找到了疾病无病状态全局渐近稳定性的阈值条件，并确定了该状态是全局稳定的。基于繁殖数的敏感性分析表明，可以通过提出的策略根除疾病。
