Abstract:
The adaptive immune system, made up of a network of cells, tissues and organs,
protect the body against infections and maintain overall health.Immunological
research has identified two types of cell interactions: thymus(T) and bone marrow(B)
derived cell interaction to explain immune responsiveness. Adaptive immune
responses are highly specific to pathogens that induce them. Cell Mediated Immunity
defend against intracellular pathogens such as viruses, intracellular bacteria and
protozoa.The T cell function lies in the heart of an efficient cytotoxic response.The
cells activation is highly regulated and is important to ensure that activation occurs in
the right context to prevent development of harmful conditions. With some key
processes of the immune system still poorly understood, construction of mathematical
models of the immune responses provide the researchers and clinicians powerful tool
for the simulation of immune system in order to increase its efficiency in the struggle
against pathogens.The purpose of this study was to establish the interplay between the
immune responses and viral pathogens.The study offers an innovative, analytical and
methodological approach in elucidating key processes of the immune responses.The
primary objectives ware: to develop a mathematical model that simulates immune
system responses to viral pathogens, analyze the stability of the model in order to get
some important ideas about the proliferation of the pathogen and to estimate the range
of parameter combinations required to mount an immune response. To achieve this a
mathematical model containing five variables: purely susceptible host cells, virus
infected cells, free virions, antibody responses and cytotoxic T lymphocyte (CTL)
response was formulated using differential equations. The simulations and analysis
was done using Matlab & Mathematica softwares, available experimental data on
Hepatitis C Virus is used to validate the analytical results. Stability analysis was
carried out using the Routh -Hurwitz method and the theory of next generation matrix
was used to determine the basic reproductive ratio as R0 = blk
adw . Threshold values of
parameters that influence immune responsiveness were also determined using the
same method. Three possible outcomes in the activation of immune responses were
considered: CTL response is established & antibody response fail, antibody response
is established & CTL response fail and both CTL & antibody responses become
established. Critical bounds are established to determine the threshold requirement
for establishment or failure of either CTL or antibody. Analytical results have shown
that when antibody response is established and CTL response fail this will represent
stable equilibrium while when both CTL and antibody responses are established it
will represent an unstable equilibrium. The numerical simulations results showed that
dominant CTL establishment is likely to clear a viral pathogen while dominant
antibody response alone may not clear the pathogen. In the case that the virus is not
cleared, viral evolution was considered, to examine how virus variation affects viral
and host survival and to understand viral disease. It was found that that CTL-induced
pathology is observed if the rate of viral replication is fast relative to the CTL
responsiveness of the host and CTL activation at this stage is not beneficial to the host
but can actually be harmful. In conclusion it is important for CTL and antibody
responses mount at the right time and strength to reduce the chances of antigenic
escape. It is recommended that the model be adopted as a tool to simulate different
treatment protocols before administering them patients.