Research Article
Mathematical Modelling of Host – Pathogen – Drug Interaction Dynamics and Immune Modulation in Viral Infection
Issue:
Volume 11, Issue 4, August 2025
Pages:
55-64
Received:
8 October 2025
Accepted:
25 October 2025
Published:
3 December 2025
Abstract: 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 R0 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 R0 = 0.659 and as CE increases, this value reduces with elasticity of ECE = -1.298 at the critical drug concentration at effect site of CE(t) = 0.72 of the dose. Simulation revealed that the most sensitive component of HAART is the PI at elasticity of Eπ = -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.
Abstract: 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...
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Research Article
Richness of Arithmetical Structure to Deliver Alternative Equations of Distance in Uniform Acceleration Motion
Teferi Mekit Dillo*
Issue:
Volume 11, Issue 4, August 2025
Pages:
65-70
Received:
22 October 2025
Accepted:
6 November 2025
Published:
9 December 2025
Abstract: The study introduces the arithmetical framework to derive classical kinematic equations without using calculus and provides comparable equations for displacement. The proposed method establishes a direct correspondence between kinematic quantities—velocity, acceleration, displacement, and time—and the elements of arithmetic progressions. Conventional calculus-based methods encounter constraints when applied to systems that suffer from accuracy; thus, it indicates that there are alternate mathematical tools and methodologies. A carefully chosen arithmetic-based model is developed, treating time as continuous when studied as a sequence and as discrete when regarded in a series. Further, acceleration is modeled as a deterministic continuous quantity, while velocity and displacement follow deterministic discrete patterns. Through transforming physical correlations directly to arithmetic patterns, this framework provides alternative distance equations. Based on standard summation, a comparative analysis of a constant-acceleration problem shows that the arithmetic model predicts displacement (47 m) with about 9% more accuracy than the classical calculus result (43 m). This confirms that the method is physically valid, and it not only makes calculations easier and reduces mistakes, but it also helps people understand motion under uniform acceleration better and gives more accurate results than the calculus-based model. The results imply that the arithmetic framework offers a unified way to connect discrete and continuous motion and gives classical mechanics a new mathematical base that makes calculations clearer. Moreover, it offers fresh methods for dealing with increasingly simplifying complex physical phenomena and advancing conceptual clarity.
Abstract: The study introduces the arithmetical framework to derive classical kinematic equations without using calculus and provides comparable equations for displacement. The proposed method establishes a direct correspondence between kinematic quantities—velocity, acceleration, displacement, and time—and the elements of arithmetic progressions. Convention...
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