https://doi.org/10.1140/epjs/s11734-024-01417-7
Regular Article
Impact of public awareness on haemo-lyphatic and meningo-encepphalitic stage of sleeping sickness using mathematical model approach
1
Department of Mathematics, Federal University Dutse, 7156, Jigawa, Nigeria
2
Department of Statistics, Jigawa State Polytechnic Dutse, 7040, Jigawa, Nigeria
3
Department of Mathematics, Prime University Abuja, Abuja, Nigeria
4
Department of Mathematics, Near East University, Cyprus, Turkey
5
Faculty of Engineering and Natural Sciences, Istanbul Okan University, Istanbul, Turkey
6
Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey
7
Department of Computer Engineering, Biruni University, Istanbul, Turkey
Received:
19
May
2024
Accepted:
14
November
2024
Published online:
4
December
2024
The parasitic disease known as sleeping sickness, or human African trypanosomiasis, is spread by vectors. Trypanosoma protozoans are the cause of it. Humans contract the parasites through the bites of tsetse flies (glossina), which have taken up the parasites from infected humans or animals. The boundedness and positivity of solutions of the proposed model have been ascertained, and the existence of equilibria has been accessed, which shows that the model consist of two equilibrium, the disease-free equilibrium and endemic equilibrium points. Using the next-generation matrix method, we calculated the control and basic reproduction number. It has been determined that the disease-free equilibrium is locally asymptotically stable if the control reproduction number is less than unity. The findings indicate that the disease-free equilibrium is globally asymptotically stable whenever the control reproduction number is less than one. A unique endemic equilibrium is contained in the model, as evidenced by the determination of the existence of endemic equilibrium. The global asymptotic stability of the endemic equilibrium point has been determined by applying the non-linear Lyapunov function of the Go-Volterra type. The findings indicate that the endemic equilibrium point is globally asymptotically stable when the control reproduction number is greater than one and when both the disease-induced death and the control reproduction number are zero. In a sensitivity analysis section, we found that 
, 
, and a are the three most sensitive parameters for increasing the transmission. On the contrary, 
and 
are the two most sensitive for reducing the spread., In the numerical simulation section, we were able to see how important is awareness on the dynamics of trypanosomiasis or sleeping sickness, as it is in numerical simulation section, public awareness was simulated to assess its importance in controlling trypanosomiasis or sleeping sickness in the society.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2024
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
