Browsing by Author "Kwach, O."

Now showing 1 - 5 of 5

Derivation and solution of the heat equation in 1-D
(International journal of engineering, science and mathematics, 2013) Kwach, O.; Ongati, Naftali O.; Alambo, David O.; 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, 2013) Kwach, O.; Ongati, Naftali O.; Nyakinda, JO.; 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 modeling of insulin therapy in patients with diabetes mellitus
(IJESM, 2015) Kwach, O.; Ongati, O.; Omolo.; Okoya, M.; Oduor.; 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) and whose solution was analyzed to provide the systems natural frequency, 0 , which is the basic descriptor of saturation level of the drug. It was established that the resonance period for the final model, that is, T 0 =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 T 0 =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
Mathematical modelling of the role of interference on the transmission dynamics and management of Hiv and Aids
(2018-09-22) Mutwiwa, Jacinta M.; Nthiiri, Joyce K.; Kwach, O.
In this paper, a deterministic mathematical model incorporating interference is developed andanalysed to investigate the role of interference on the transmission dynamics and managementof HIV and AIDS. The model is shown to be positively invariant as well as bounded. Theendemic state is shown to exist provided that the reproduction number is greater than unity.Furthermore, by the use of Routh-Hurwitz criterion and suitable Lyapunov functions, theendemic states are shown to be locally and globally asymptotically stable. This implies thatdisease transmission levels can be kept quite low or manageable with minimal deaths at the peaktimes of the re-occurrences. Numerical simulations indicate that minimal interference againstthe disease lowers the rate of infection and enhances the disease management.
The role of teachers in implementing eﬀective play in early childhood and educational centers
(Lap lambert academic publishing, 2013) Kwach.; Alphonce, O.; Kwach, O.; Ogwan’g, Isabel.
Over the last several years, there has been an increased focus on school readiness and supporting children during the preschool years to learn the skills they need to be successful in elementary school and beyond (Bowman, Donovan, Bums, et al., 2000; Shonkoff & Phillips, 2000). The capacity to develop positive social relationships, to concentrate and persist on challenging tasks, to effectively communicate emotions, and to problem solve are just a few of the competencies young children need to be successful as they transition to school. In this article, we describe the Teaching Pyramid (Fox, Dunlap, Hemmeter, Joseph, & Strain, 2003), a model for promoting young children's social-emotional development and addressing children's challenging behavior and its link to critical outcomes for children, families, and early childhood programs. The Pyramid includes four components: building positive relationships with children, families, and colleagues; designing supportive and engaging environments; teaching social and emotional skills; and developing individualized interventions for children with the most challenging behavior. Given the unique characteristics of early childhood settings, implementation issues and implications of the model are a primary focus of the discussion.