Mathematical Modeling of Tuberculosis Transmission Dynamics in Ethiopia

Seyid, Moksina

dc.contributor.author	Seyid, Moksina
dc.date.accessioned	2024-07-24T10:26:35Z
dc.date.available	2024-07-24T10:26:35Z
dc.date.issued	2024-06
dc.identifier.uri	http://ir.bdu.edu.et/handle/123456789/15897
dc.description.abstract	Tuberculosis (TB) remains a major global health concern, characterized by chronic air borne transmission. This study develops and analyzes a nonlinear, deterministic mathe matical model for TB dynamics in Ethiopia. The model categorizes the population into six compartments: susceptible, vaccinated, exposed, infected, treated, and recovered, incorpo rating vaccination and treatment interventions. We determine disease-free and endemic equilibrium points, computing the reproduction number using the next-generation matrix approach. Stability analysis shows that the disease-free equilibrium is locally and globally asymptotically stable when the reproduction number is less than one, while the endemic equilibrium is locally and globally asymptotically stable if the reproduction number greater than one. Sensitivity analysis identifies recruitment, contact, and infection rates as crit ical parameters influencing the reproduction number. Numerical simulations based on WHO data, reports, and websites reporting epidemiological health statistics in Ethiopia as well as from related published articles underscore the significant role of contact and in fection rates in disease spread. Parameter estimation of the contact and transmission rate through minimum search algorithm and maximum likelihood techniques using R software enhances the model’s accuracy for TB dynamics in Ethiopia. Using MATLAB software we obtained interesting simulation results which indicate that combination of increased vaccination and treatment rate has a great contribution in combating TB. It is worth mentioning that the simulation results confirm the conclusion drawn from the qualitative analysis of the model. Hence, we came to realize that the number of infected people keeps decreasing if one carefully combines vaccination with appropriate treatment and decrease the contact between susceptible and infected individuals. The study recommends for gov ernment policymakers to effective TB control in Ethiopia can be achieved by optimizing treatment, vaccination, and recovery strategies to minimize transmission rates..	en_US
dc.language.iso	en_US	en_US
dc.subject	Mathematics	en_US
dc.title	Mathematical Modeling of Tuberculosis Transmission Dynamics in Ethiopia	en_US
dc.type	Thesis	en_US