Modelling the Impact of Trapping Blackfly Vectors on the Transmission of Onchocerciasis

Subject Areas : International Journal of Mathematical Modelling & Computations

Julius Tumwiine ¹ (Department of Mathematics, Mbarara University of Science and Technology, Mbarara, Uganda)
Raymond Muhumuza ² (Department of Mathematics, Mbarara University of SCience and Technolog. Mbarara, Uganda)

Received: 2020-08-26 Accepted : 2020-10-20 Published : 2020-12-01

Keywords: Sensitivity analysis, Basic reproduction number, endemic equilibrium, river blindness, Vector control‎,

Abstract :

Onchocerciasis, usually referred to as river blindness, a skin and eye parasitic infestation is caused by the filarial nematode Onchocerca volvulus. Current control and eradication efforts are being frustrated by the continued existence and thriving of blackflies which are the disease transmitting vectors that breed along the banks of fast flowing and highly oxygenated rivers and streams. This study aims at assessing the effect of using vector traps on the transmission and control of onchocerciasis. A host-vector deterministic model which incorporates vector trapping by use of a system of ordinary differential equations is developed. The model is analysed for steady states and the basic reproduction number is obtained using the next generation method. It is found that the disease free steady state is stable if the basic reproduction number R0<1. There exists a unique endemic equilibrium which is locally and globally asymptotically stable if R0>1. Numerical simulations show that trapping the blackfly vectors has an effect on the spread and control of the disease. However, it is discovered that using traps alone is not a sufficient strategy and needs to be combined with other methods if the disease is to be completely wiped out of the population.