Browsing by Author "Ongati, Omolo"

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Derivation and solution of the heat equation in 1-D
(International Journal of Engineering, Science and Mathematics, 2013-06-01) Kwach, Boniface Otieno; Ongati, Omolo; Alambo, David; Okaka, Colleta A.
Heat flows in the direction of decreasing temperature, that is, from hot to cool. In this paper we derive the heat equation and consider the flow of heat along a metal rod. The rod allows us to consider the temperature, u(x,t), as one dimensional in x but changing in time, t.
Forensic estimation of time of death: a mathematical model
(International Journal of Management,IT and Engineering (IJMIE), 2013-07-01) Kwach, Boniface Otieno; Ongati, Omolo; Nyakinda, J.O.; Nyang’inja, Rachael
In this paper we establish the exact time of death of a murdered person. This leads to an ordinary differential equations whose solution has been analyzed to provide the approximate time of death. Forensic expert will try to estimate this time from body’s current temperature and calculating how long it would have taken to lose heat to reach this point. This provides an accurate approach to establish the approximate time when crime is committed.
Mathematical model for detecting diabetes in the blood
(Academia, 2011-07-01) Kwach, Boniface Otieno; Ongati, Omolo; Simwa, Richard
This study presents a new mathematical model for Blood Glucose Regulatory System(BGRS) which includes epinephrine as a third variable in the form, Ў= AY, and whose solution has been analyzed for equilibrium and stability to provide the blood glucose concentrations for diabetics and non-diabetics. We establish that the final model is asymptotically stable compared to the existing models, that is, the eigenvalues of the coefficient matrix are complex numbers with negative real parts. Furthermore, the resonance period for the final model, that is, T0 = 2:9847134 hours, is far less than that of the existing model, showing that the glucose concentration returns to normal level within a shorter time.
Mathematical model for drug therapy in patients with diabetes mellitus
(International Journal of Engineering, Science and Mathematics, 2013-03-01) Kwach, Boniface Otieno; Ongati, Omolo; Okoya, Oduori; Otedo, Amos
This study presents a new mathematical model for Drug Therapy in Patients with Diabetes Mellitus which includes external rate at which blood glucose, insulin and epinephrine is being increased in the form Y= fi (g,h,e)+ri (t) . The system has been analyzed and solved to provide the systems natural frequency, ω0, which is the basic descriptor of saturation level of the drug. We establish that the resonance period for the final model, that is, T0=3.76912 hrs, agrees well with the data for the existing insulin therapy, showing that the peak, which is the time period for insulin to be most effective in lowering blood sugar, is in the acceptable therapeutic range
Mathematical modeling of insulin therapy in patients with diabetes mellitus
(International Journal of multidisciplinary sciences and Engineering, 2015-06-01) Kwach, Boniface Otieno; Ongati, Omolo; Okoya, Oduori; Otedo, Amos
This study presents a Mathematical Model Insulin Therapy in Patients with Diabetes Mellitus which includes external rate at which blood glucose, insulin and epinephrine are being increased in the form, (Y=AY+r ⃗(t)) ̇ andwhose solution was analyzed to provide the systems natural frequency, ω_o which is the basic descriptor of saturation level of the drug. It was established that the resonance period for the final model, that is, T0=3.76912 hrs, is in the acceptable therapeutic range and agrees well with the data for the existing insulin therapy. By employing the model, it is shown that, the peak, which is the time period for insulin to be most effective in lowering blood sugar, is shorter than T0= 5.3199 hrs, for the existing model. This model would help the medical practitioners to predict drug therapy in patients with Diabetes Mellitus, in such a way that the concentration of the drug remains in the therapeutic range.