Research Article African Trypanosomiasis Dynamics: Modelling the Effects of Treatment, Education, and Vector Trapping Yustina A. Liana , 1 Nyimvua Shaban, 1 Goodluck Mlay, 1 and Anitha Phibert 2 1 Department of Mathematics, University of Dar es Salaam, Dar es Salaam, Tanzania 2 Department of Zoology and Wildlife Conservation, University of Dar es Salaam Postal address, P.O.Box 35062, Dar es Salaam, Tanzania Correspondence should be addressed to Yustina A. Liana; lianayustina@yahoo.com Received 21 May 2020; Revised 2 November 2020; Accepted 12 November 2020; Published 26 November 2020 Academic Editor: Ra´ ul E. Curto Copyright © 2020 Yustina A. Liana et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Africantrypanosomiasisisavector-bornediseasethatismainlytransmittedbyinfectedtsetseflies.Adeterministicmodeloftsetse flyvector,human,andcattlehostsisformulatedandanalyzedtogaininsightsintothediseasedynamics.erolesofpublichealth education, treatment, and tsetse fly traps are studied. e effective reproduction number, a threshold used to determine whether the disease persists or dies out in the population, is determined. e sensitivity analysis of the model parameters is performed to determine their relationship with the effective reproduction number. e results show that the tsetse fly biting rate is the most sensitive parameter to the effective reproduction number. Furthermore, the model’s numerical simulation shows that a com- binationofallthreeinterventionshasthemostsignificantimpactonthecontrolofAfricantrypanosomiasis.us,werecommend that these control measures be put concurrently in endemic areas for effective control of the disease transmission. 1. Introduction African trypanosomiasis is a disease caused by microscopic parasites of the species Trypanosoma brucei, and it is trans- mitted through bites of infected tsetse flies of the genus Glossina which are most common in woodland and savannah areas of sub-Saharan Africa. Trypanosomabrucei infects both humans and animals, and if not treated early, it can lead to death [1]. Human African trypanosomiasis (HAT) is caused by Trypanosoma brucei gambiense and Trypanosoma brucei rhodesiense while African animal trypanosomiasis (AAT) is mainly caused by Trypanosoma brucei vivax, Trypanosoma brucei congolense, and Trypanosoma brucei rhodesiense [2]. Even though both humans and animals are infected by Trypanosoma brucei, cattle are mostly infected because of tsetse flies’ feeding preferences. Both male and female tsetse flies can transmit Trypanosoma and depend only on hosts’ blood to survive or for all their nutritional needs, unlike other vector-borne diseases such as malaria, where only a female mosquito can feed on blood and can transmit the disease [3]. e disease has affected at least 37 countries in sub- Saharan Africa, threatening the lives of millions of people in rural areas. Around 10 million square kilometers in sub- Saharan Africa have been affected by Trypanosoma brucei species [3]. On average, 70,000 cases of HAT are reported each year in sub-Saharan Africa, and more than 1 million cattle die every year due to trypanosomiasis and cause an economic loss of between $2 and $4.5 billion annually [4, 5]. Itisclaimedthatthehighmortalityrateoflivestockcanlead to low production of meat and milk up to 50% in sub- Saharan Africa every year [6]. So far, much work has been done to investigate the dynamics of African trypanosomiasis. For example, Moore et al. [4] developed a model on the effect of climate change on African trypanosomiasis dynamics. e result from their study predicted that, by the year 2090, about 46–77 million people would be exposed to trypanosomiasis disease. Otieno et al. [7] studied the dynamics of trypanosomiasis in a cattle population by including the wild animals as an alternative feeding source for tsetse flies. e results obtained from the Hindawi International Journal of Mathematics and Mathematical Sciences Volume 2020, Article ID 3690472, 15 pages https://doi.org/10.1155/2020/3690472