Malthus-Informed Drug Development (MIDD)

The 19th century scholar Thomas Robert Malthus is widely regarded as the founder of the discipline of population modeling, although 600 years before him, Leonardo of Pisa (more widely known as Fibonacci) presented a mathematical model to describe the growth of rabbits. In his Essay on the Principle of Population, Malthus presented a simple model that describes how the human population grows exponentially, whereas food production can only increase linearly. The predictions of this model, which became known as “Malthusian catastrophes,” are grim: cycles of population growth inevitably followed by famine and collapse.¹ Malthus' original model has been the subject of intense debate, and its flaws are widely recognized. Despite its obvious shortcomings, the Malthus model has been the basis for foundational work in a variety of scientific areas such as economics, demographics, and climate change.² However, the impact of Malthus' work in clinical pharmacology has not received much attention, although it can be argued that several fundamental pharmacokinetic–pharmacodynamic (PKPD) principles have, at least indirectly, their roots in it.

For example, after the publication of Malthus' original work, it was soon agreed that growth is typically not unbounded but capped by a maximum population size. This insight was the basis for Pierre François Verhulst to introduce the logistic growth model, which included a “carrying capacity”—the maximum population size that an environment can sustainably support. The logistic equation proposed by Verhulst is the basis for the most widely used model in pharmacology and PKPD, often referred to as the E_max model or Hill equation, which is equivalent to equations proposed by, amongst others, Langmuir and Michaelis–Menten in the fields of chemistry and enzymology.^{1, 3-5}

Another main branch that developed from the Malthus model was the work from Lotka and Volterra, who independently derived what has become known as the “predator–prey” model, adding a second species to the Malthusian population mix.⁶ These models became the basis for studying and predicting drug effects in infectious diseases caused by, for example, human immunodeficiency virus (HIV), hepatitis B (HBV) and C virus (HCV), and coronaviruses (Figure 1).^{7, 8} For example, in their seminal paper, Neumann and co-workers proposed a basic model of viral infection based on Malthusian principles to unravel the dynamics of HCV and the mechanism of action of interferon.⁹ This work became the foundation for model-informed drug development (MIDD) in HCV and has been widely used to optimize clinical trial design and individualized dosing (Figure 2).^{7, 8}

In the current issue of Clinical Pharmacology & Therapeutics (CPT), Cortés-Rio et al. provide an example of how these earlier models of viral infection dynamics can be expanded to incorporate the influences of host immune components and pharmacotherapies on virion production, resulting in a framework which more comprehensively describes viral infection dynamics, predicts patient treatment outcomes, and identifies clinical treatment response biomarkers.¹⁰ They developed a mechanistic computational model of HBV which incorporates the influences of host immune responses and standard-of-care therapies (nucleos(t)ide analogues and pegylated interferon) on both infection dynamics and host prognostic/treatment response biomarkers, such as serum HBV surface antigen levels (Figure 2). The model was used to run an in silico ‘virtual’ trial, assessing if clinical treatment responses could be simulated. The virtual trial was found to robustly predict real-world patient response - functional cure - to standard-of-care therapies, thus providing evidence for the positive impact potential of mechanistic platforms in MIDD for viral diseases.

It has been proposed that the probability of success in drug development for infectious diseases is ~3-fold higher if a biomarker is available.¹¹ Cortés-Rio and co-workers show that virtual patients enabled the generation of large virology biomarker synthetic datasets, which empowered a machine learning model to predict functional cure in virtual patients with ~95% accuracy. Despite recent progress in optimizing interferon-based treatment and vaccine strategies^{12, 13}, and the emergence of novel therapeutics such as short-interfering RNAs¹⁴, the medical need in HBV remains high, with almost 1 million people dying from it every year.^{12, 14}

Lack of reproducibility of complex mechanistic models has been a significant issue, as reported by, for example, Kirouac et al.¹⁵ and Tiwari et al.¹⁶ CPT, like many other journals, therefore, expects authors to make model code available online as supplementary material with a manuscript. Cortés-Rio et al. have set a new standard for this, with a 50-page appendix to their paper serving as a detailed tutorial for their model. It is so comprehensive that it could have been published as a standalone paper, but the CPT editorial team felt that keeping the original manuscript and technical appendix together would better serve our readers. We applaud Cortés-Rio and co-workers for raising the bar not only for HBV MIDD, but also for publication standards for mechanistic models in general.

No funding was received for this work.

The author declared no competing interests for this work.