Modelling the transmission dyanamics of Leptospirosis with control measures
| dc.contributor.author | Kasebo, Ndabazi Abdallah | |
| dc.date.accessioned | 2023-03-31T11:32:40Z | |
| dc.date.available | 2023-03-31T11:32:40Z | |
| dc.date.issued | 2022 | |
| dc.description | Dissertation (MSc Mathematics) | en_US |
| dc.description.abstract | Leptospirosis is a bacterial disease which is caused mainly by rodents and other animals. The disease is more neglected in many parts of the world. Major hosts of leptospirosis are rodents and other small animals like bats. In this dissertation, SIR model studied humans and animals leptospirosis transmission dynamics with control measures. The model shows direct transmission of the disease in human and animals. Also the model with control strategies is formulated, controls involved are treatment of infected humans, treatment and quarantine of infected animals both by using antibiotics such as doxycycline or penicillin and intravenous antibiotics may be administered for persons and animals with severe symptoms and rat control by trapping and killing them which also involves poisoning them. Disease free and endemic equilibrium are calculated and their local and global stabilities are determined. Trace-determinant method is used to find out local stability of disease free equilibrium point while Lyapunov function technique is used to determine global stability of both, disease free and endemic points. Basic reproduction number , R0 = 0:0178 and effective reproduction number, Re = 0:000319 are calculated by next generation method. The Lyapunov method was used to determine the global stability of the model computations. The model was computed numerically by Runge-Kutta method and computation by using Maple software. Simulation of the model results is done by using MATLAB. The sensitivity of R0 shows that the rate of pathogens sheds by infected animals into the environment is high, that means animals play a big role on shedding bacteria than rats. Also it shows animal to animal transmission of leptospirosis is very high comparing to other forms of transmission. Solutions show that, the disease free equilibrium point E0 is locally asymptotically stable whenever R0 < 1 and unstable when R0 > 1, while endemic equilibrium point E_ is globally asymptotically stable when R0 > 1. The numerical simulations presented to illustrate the dynamics transmission of the disease, the simulation shows that the environment is the main way for both human and animals to contract leptospirosis. The suggested controls are treatment of infected humans, treatment and quarantine of infected animals and rat control by trapping and killing as well as poisoning them. The results shows that treatment and quarantine of infected animals is more effective strategy than treatment of infected humans. | en_US |
| dc.identifier.citation | Kasebo, N. A. (2022). Modelling the transmission dyanamics of Leptospirosis with control measures (Master's dissertation). The University of Dodoma, Dodoma. | en_US |
| dc.identifier.uri | http://hdl.handle.net/20.500.12661/3640 | |
| dc.language.iso | en | en_US |
| dc.publisher | The University of Dodoma | en_US |
| dc.subject | Leptospirosis | en_US |
| dc.subject | Doxycycline | en_US |
| dc.subject | Penicillin | en_US |
| dc.subject | Bacterial disease | en_US |
| dc.subject | Disease transmission | en_US |
| dc.subject | Animal infectious disease | en_US |
| dc.subject | Endemic equilibrium | en_US |
| dc.title | Modelling the transmission dyanamics of Leptospirosis with control measures | en_US |
| dc.type | Dissertation | en_US |