Mathematical Model Analysis and Simulation of Visceral Leishmaniasis, Kashgar, Xinjiang, 2004–2016

Visceral leishmaniasis (VL), known as kala-azar, is a serious parasitic disease. After malaria, VL is the second largest parasitic killer. This paper focuses on the VL transmission around sandflies, dogs, and people. Kashgar is located on the southwestern edge of Xinjiang, where kala-azar parasite infection occurs every year. According to the cases reported in the Kashgar Prefecture from 2004 to 2016, we proposed a dynamic model based on these three populations. The SEIR model was established for human population, the SI model was established for sandfly population, and the SI model was established for dog population. We fitted the model to cumulative cases from 2004 to 2016 for the epidemic in Kashgar and predicted that the cumulative incidence of kala-azar in Kashgar would continue to increase, but its growth rate would gradually slow down, which means that the number of cases would gradually decrease every year. We also estimated the basic reproduction number  = 1.76 (95% CI: 1.49–1.93). The sensitivity analysis shows that the mutual infection between sandfly and dog contributes the most to the basic reproduction number, while the transmission proportion of sandfly to the susceptible person and the mutual infection between sandfly and dog contribute the most to the number of leishmaniasis human cases. Therefore, according to the sensitivity analysis results, reducing the contact between sandflies and dogs is an effective way to reduce kala-azar.