Analysis of a TB/HIV co-infection model with vertical transmission and treatment
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Date
2021
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Publisher
University of Namibia
Abstract
In this mini thesis, we developed a new mathematical model for the dynamics of HIV /TB co infection in a population with treatment and vertical transmission. TB and HIV sub-models
are derived from the full model and analyzed separately. The aim was to use mathematical
modeling to find favorable conditions under which the diseases can be stopped from spreading
further in the population. The models are built with a motive to study the dynamic behavior
of the trajectories which has the potentials to guide TB and HIV control. The study used
the Routh-Hurwitz criteria to conclude on the stability of the system. The basic reproduction
numbers for TB (Rr) and HIV (RH ) are computed using t he next generation matrix method,
and the basic reproduction number R 0 = max{R r, RH} of the full model is also provided.
From the study, it was established that if R o < 1 then the disease-free equilibrium is stable,
and the disease dies out; if R r < 1 and RI-I > 1, then the HIV is endemic and TB dies out;
however if RH < 1 and Rr > 1, then TB is endemic and HIV dies out; in addition, if R r > 1
and RH > 1, the two diseases persist in the population. Sensitivity analysis of the basic re production number for TB-only model with respect to the model parameters was carried out.
Results from quantitative analysis revealed t hat, increasing treatment rate for bot h HIV and T B significantly reduces t he values of the basic reproduction number. The study concluded that,
decreasing the probability rate of transmission of HIV /AIDS and TB leads to the decrease of
the population of infectives. Furthermore, by controlling the probability rate of transmission,
t he spread of the disease can be reduced significantly. Effective treatment for TB breaks the
cycle of transmission. TB individuals must be identified and treated in order to reduce further
spread of TB in human population
Description
A thesis submitted in partial fulfilment of the requirements for the Degree of Master of Science in Applied Mathematics
Keywords
Next-Generation matrix method, Basic reproduction number, Routh-Hurwitz cri teria, Disease-free equilibrium, Sensitivity analysis, HIV /TB co-infection