MATHEMATICAL ANALYSIS OF THE ROLE OF DETECTION RATE IN THE DYNAMICAL SPREAD OF HIV-TB CO-INFECTION
Journal Title: JOURNAL OF ADVANCES IN MATHEMATICS - Year 2016, Vol 11, Issue 10
Abstract
Human Immunodeficiency Virus (HIV) co-existing with Tuberculosis (TB) in individuals remains a major global health challenges, with an estimated 1.4 million patients worldwide. These two diseases are enormous public health burden, and unfortunately, not much has been done in terms of modeling the dynamics of HIV-TB co-infection at a population level. We formulated new fifteen (15) compartmental models to gain more insight into the effect of treatment and detection of infected undetected individuals on the dynamical spread of HIV- TB co-infection. Sub models of HIV and TB only were considered first, followed by the full HIV-TB co-infection model. Existence and uniqueness of HIV and TB only model were analyzed quantitatively, and we shown that HIV model only and TB only model have solutions, moreover, the solutions are unique. Stability of HIV model only, TB model only and full model of HIV-TB co-infection were analyzed for the existence of the disease free and endemic equilibrium points. Basic reproduction number () was analyzed, using next generation matrix method (NGM), and it has been shown that the disease free equilibrium point is locally asymptotically stable whenever and unstable whenever this threshold exceeds unity. i.e., Numerical simulation was carried out by maple software using differential transformation method, to show the effect of treatment and detection of infected undetected individuals on the dynamical spread of HIV-TB co-infection. Significantly, all the results obtained from this research show the importance of treatment and detection of infected undetected individuals on the dynamical spread of HIV-TB co-infection. Detection rate of infected undetected individuals reduce the spread of HIV-TB co-infections.
Authors and Affiliations
SUNDAY OLUMUYIWA Adewale, I. A Olopade, I. T Mohammed, S. O Ajao, O. T Oyedemi
Keywords
Related Articles
- EP ID EP651633
- DOI 10.24297/jam.v11i10.800
- Views 140
- Downloads 0
A New Inexact Non-Interior Continuation Algorithm for Second-Order Cone Programming
Second-order cone programming has received considerable attention in the past decades because of its wide range of applications. Non-interior continuation method is one of the most popular and efficient methods for solvi...
Modeling Vanilla Option prices: A simulation study by an implicit method
Option contracts can be valued by using the Black-Scholes equation, a partial differential equation with initial conditions. An exact solution for European style options is known. The computation time and the error need...
ALGEBRAIC PROOF IV FERMATS LAST THEOREM
The special case z4 = x4 + y4 is impossible [1]. In view of this fact, it is only necessary to prove, if x, y, z, are relatively prime positive integers, π is an odd prime, zπ = xπ +yπ (In this artic...
Intransitive Permutation Groups with Bounded Movement Having Maximum Degree
Let G be a permutation group on a set with no fixed points in and let m be a positive integer. If for each subset of the size is bounded, for , we define the movement of g as the max over...
Existence and uniqueness of mild solutions of nonlinear difference-integrodifferential equation with nonlocal condition
In this paper we investigate the existence, uniqueness and continuous dependence of solutions of the difference-integrodifferential equations. The results are obtained by using the well known Banach fixed point theorem,...