Mathematical models of trypanosoma brucei rhodesiense disease transmission and control strategies

Abstract

Human African Trypanosomiasis (HAT), also known as sleeping sickness is a neglected dis ease that impacts 70 million people living in 1.55 million km2 in sub-Saharan Africa. The disease strikes predominantly poor populations in sub-Saharan Africa and has been targeted for elimination as a public health problem by 2030. Despite decades of control operations, the disease remains enigmatic and persists in populations at low levels of prevalence. Hence sev eral research approaches must be utilized to infer on the feasibility of attaining the set target. Among them, mathematical modeling is a very successful tool and has been extensively used for different diseases. In this study four mathematical models were proposed to evaluate the effects of educational campaigns, seasonality, memory effects, time delay and heterogeneity in the human population on Trypanosoma brucei rhodesiense transmission and control dynamics. In the formulated models the basic reproduction number R0 was computed and qualitatively used to establish the condition for disease eradication and persistence. In the first model, effects of human awareness through educational campaigns and use of insecticides on short-and long-term dynamics of the disease were evaluated. Analytical results of the study showed that the model undergoes a backward bifurcation. Further, upon extending the model to incorporate time-dependent educational campaigns and the use of insecticides, it was noted that when the aforementioned strategies were intensified the associated costs were also high, and the reverse was true. Moreover, it was also noted that reducing the upper bound of educational campaign control (u1) from 1 to 0.5 and insecticide control (u2) from 1 to 0.3 could lead to a 17.6% reduction in costs. Next, the model system was extended to include temperature and case detection followed by treatment of infected humans. With the aid of suitable Lyapunov functionals, the global stability of the model’s steady states was carried out. Upon simulating the model with temperature fixed at 20 and 25◦C, it was noted that the value of vector control be greater than 30 and 50% respectively for R0 to be less than unity. Lastly, the time delay factor was included in the model system to assess the effects of incubation period on the dynamics of T. brucei rhodesiense disease in the population. The numerical results demonstrated that the inclusion of the time delay factor in the model system destabilized the endemic equilibrium point leading to Hopf bifurcation.