Mathematical Modelling of Host – Pathogen – Drug Interaction Dynamics and Immune Modulation in Viral Infection

Viral infections target the same immune system cells which fight against the infection, significantly curtailing the capacity of the body to fight associated diseases. Once the virus successfully infects a cell, it uses the same highly proliferating immune host cells to multiply, and enjoy host immunity. With the absence of HIV treatment, available chemotherapy is used to boost immune system, inhibit infection, and disrupt the assembling of viral materials during reproduction. This is achieved by use of Highly Active Anti-Retroviral Therapy (HAART) which contains immune proliferation boosters, reverse transcriptase inhibitors (RTI) and Protease Inhibitors (PI) components. In this paper, a host-pathogen-drug interaction triangle mathematical model is formulated to depict the effect of chemotherapeutic control on reproductive ratio. A SEIR paradigm was used and modified to show differentiated adaptive immune T and B cells, and a viral load compartment. Reproductive ratio <I>R<sub>0</sub></I> was computed using the next generation matrix, together with its elasticity to control parameters. It was found that in absence of any controls, the reproductive ratio R<sub>0</sub> = 0.659 and as C<SUB>E</SUB> increases, this value reduces with elasticity of E<SUB>CE</SUB> = -1.298 at the critical drug concentration at effect site of C<SUB>E</SUB>(t) = 0.72 of the dose. Simulation revealed that the most sensitive component of HAART is the PI at elasticity of E<sub>π</sub> = -1.573, followed by the drug potency to directly kill viral materials ω, closesly followed by the drug potency to kill infected immune cells ψ and lastly by the RTI’s ability to prevent infection η. In conclusion, correct composition of HAART and consist dosing to maintain therapeutic window concentration reduces the viral load, boosts the immune system to normalcy, and generates a pool of memory cells, ready for immediate attack in the subsequent re-infection. This restores the health of People Living with HIV/AIDS (PLWHA), reduces the force of infection of susceptible cells and consequently reduce disease incidence rate across the population.