Stability Analysis of the Mathematical Model for the Dynamics of Diabetic Population under the Combine Effect of Birth Rate and Treatment

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Author(s) Ibrahim Isa Adamu | A.A. Momoh, A. Tahir
Pages 26-35
Volume 5
Issue 1
Date January, 2016
Keywords Panmictic, Population, Diabetes, Birth Rate, Fasting Blood Sugar, Random Blood sugar
Abstract

In this paper a mathematical model for the dynamics of diabetic population under the combined effect of birth rate and treatment was developed to study the stability and disease free equilibrium of the diabetic population. In developing the model, we splitted the population of diabetics into; Diabetics without complications, diabetics with complications, diabetics with regulated glucose as a result of treatment, and severely disabled sub-populations, we then modeled the dynamics between the first three sub-populations, this ushered in a model consisting of three differential equations. We obtained the disease free equilibrium state of the model and carried out stability analysis. The result of the study established that; birth rate and the number of diabetics with complications determine the equilibrium solutions, and that the contribution of birth rate to the dynamics of the diabetic population depends on the dynamics of the diabetic gene and life style. This is in tandem with the dynamics of the diabetics since diabetes is not contagious, rather, a genetic disorder with chromosomes 1q21-1q24, 2q37, 12q24, and chromosome20, as the locus that harbor the gene that causes diabetes. The work recommended that efforts should be geared towards controlling life style and reproductive practice of a population to curtail the genetic spread of the disease.

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