Browsing by Author "Nyaberi, Halson Ogeto"

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    Mathematical Modeling of Cholera Transmission with Education Campaign and Treatment Through Quarantine
    (Kenyatta University, 2019-06) Nyaberi, Halson Ogeto
    Cholera, a water-borne disease characterized by intense watery diarrhea, a ects people in regions with poor hygiene and untreated drinking water. This disease remains a menace to public health globally and it is capable of causing high death rates if not adequately controlled, leading to loss of individuals who are engaged in development projects and hence crumbling communities' progress. In this research, we derived a system of ordinary di erential equations from SIQR-B mathematical model to study the dynamics of cholera transmission with health education campaign and treatment through quarantine as con- trols against epidemic in Kenya. The e ective basic reproduction number is computed using the next generation matrix method. The equilibrium points of the model are deter- mined and their stability is analysed. Results of stability analysis show that the disease free equilibrium is both locally and globally asymptotically stable R0 < 1 while the en- demic equilibrium is both locally and globally asymptotically stable R0 > 1. Numerical simulation carried out using MATLAB software shows that when health education cam- paign is e cient, the number of cholera infected individuals decreases faster, implying that health education campaign is vital in controlling the spread of cholera disease.
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    Mathematical Modeling of the Dynamics of Infectious Diseases with Relapse
    (International Knowledge Press., 2020) Nyaberi, Halson Ogeto; Wakwabubi, Victor Wangila
    In this paper, we have formulated a mathematical model based on a series of ordinary dierential equations to study the transmission dynamics of infectious diseases that exhibit relapse. The basic reproduction number of the model was computed using the next generation matrix method. The existence of the equilibrium points of the model was investigated and stability analysis carried out. The disease free equilibrium point was found to be locally asymptotically stable when R0 < 1 and unstable when R0 > 1 and globally asymptotically stable when R0 < 1 and unstable when R0 > 1. The endemic equilibrium point was found to be locally and globally asymptotically stable when R0 > 1. The center manifold theory was used to investigate the type of bifurcation at R0 = 1.