Abstract:
Infectious diseases have become problematic throughout the world, threatening
individuals who come into contact with pathogens responsible for transmitting
diseases. Pneumoccocal pneumonia, a secondary bacterial infection follows an
influenza A infection, responsible for morbidity and mortality in children, the elderly, and immuno–comprised groups. The aims of this Thesis are to; develop a mathematical model for within-host co-infection of influenza A virus and pneumococcus,
model between–host pneumococcal pneumonia in order to determine the effect
of time delays due to latency and seeking medical care, and study the effect of
antibiotic resistance awareness and saturated treatment in the control of pneumococcal pneumonia. Analysis of the stability of steady states of influenza A virus
and pneumococcal co-infection, pneumococcal pneumonia with time delays, and
antibiotic resistance awareness is done. The graph theoretic method, combined
linear and quadratic Lyapunov functions, and the Goh–Voltera Lyapunov function are
used to get suitable Lyapunov functions for global stability of steady states. The
results show that the endemic equilibrium of pneumococcal pneumonia is locally
stable without delays and stable if the delays are under conditions. The results
suggest that as the respective delays exceed some critical value past the endemic
equilibrium, the system loses stability and yields Hopf–bifurcation. The results
of influenza A virus and pneumococcal co-infection show that there exists a
biologically important steady state where the two pathogens of unequal strength
co-exist and replace each other in the epithelial cell population when the pathogen
fitness for each infection exceeds unity. The impact of the influenza A virus onto
pneumococcus and vice–versa yields a bifurcation state. The results show that
the presence of antibiotic resistance awareness and treatment during the spread
of pneumococcal pneumonia drastically reduces the basic reproduction number
R0 to less than unity, hence the disease could be eradicated.
