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<p>Drug toxicity and therapeutic effects are two concepts in pharmacokinetics that coexist in conflict. Too much or an insufficient amount of the drug in the body is not ideal. This brings about the need to optimise these two contrasting but important factors. As such, we developed a system of three ordinary differential equations to describe the dynamics of drug concentration, taking into account the effect of drug-metabolising enzymes and periodic intravenous injections, using the Dirac Delta function as the source term. We noted that frequent administration of drugs helps achieve the minimum level of drug efficacy. The model with a single dose has (0, 0, 0) as the only stable equilibrium point. However, when periodic injections are administered, this equilibrium is destroyed, and a new stable non-zero equilibrium point emerges.</p>

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Mathematical modelling of drug elimination by drug metabolising enzymes with periodic intravenous injections

  • 期刊论文

  • 发表日期：

    2026年7月30日

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  • Bradley J. Mathe,
  • Mlamuli Dhlamini,
  • Kukhanya Zondo,
  • Hiranmoy Mondal,
  • Noble J. Malunguza,
  • Mbakisi Dube

摘要

Drug toxicity and therapeutic effects are two concepts in pharmacokinetics that coexist in conflict. Too much or an insufficient amount of the drug in the body is not ideal. This brings about the need to optimise these two contrasting but important factors. As such, we developed a system of three ordinary differential equations to describe the dynamics of drug concentration, taking into account the effect of drug-metabolising enzymes and periodic intravenous injections, using the Dirac Delta function as the source term. We noted that frequent administration of drugs helps achieve the minimum level of drug efficacy. The model with a single dose has (0, 0, 0) as the only stable equilibrium point. However, when periodic injections are administered, this equilibrium is destroyed, and a new stable non-zero equilibrium point emerges.