Temperature is one of the integral environmental drivers that strongly affect the distribution and density of tsetse fly population. Precisely, ectotherm performance measures, such as development rate, survival probability and reproductive rate, increase from low values (even zero) at critical minimum temperature, peak at an optimum temperature and then decline to low levels (even zero) at a critical maximum temperature. In this study, a fractional-order Trypanosoma brucei rhodesiense model incorporating vector saturation and temperature dependent parameters is considered. The proposed model incorporates the interplay between vectors and two hosts, humans and animals. We computed the basic reproduction number and established results on the threshold dynamics. Meanwhile, we explored the effects of vector control and screening of infected host on long-term disease dynamics. We determine threshold levels essential to reducing the basic reproduction number to level below unity at various temperature levels. Our findings indicate that vector control and host screening could significantly control spread of the disease at different temperature levels.

温度是强烈影响采采蝇种群分布和密度的不可或缺的环境驱动因素之一。精确地，诸如温度，存活率和繁殖率之类的外温性能指标在临界最低温度下从低值（甚至为零）增加，在最佳温度下达到峰值，然后在临界最高温度下下降到低水平（甚至为零）。 。在这项研究中，分数阶布氏锥虫罗得氏菌考虑了包含矢量饱和度和温度相关参数的模型。所提出的模型结合了载体与两个宿主（人和动物）之间的相互作用。我们计算了基本繁殖数量，并在阈值动态方面建立了结果。同时，我们探讨了载体控制和感染宿主筛选对长期疾病动态的影响。我们确定了在各种温度水平下将基本复制数量降低到低于1所必需的阈值水平。我们的发现表明，在不同温度水平下，病媒控制和寄主筛选可以显着控制疾病的传播。