A Multi-Modal Small-Molecule Architecture for Heterogeneous Tumours and Chronic Viral Reservoirs: Mechanistic Model, Analytic Eradication Criterion, and a Falsifiable Quantitative Specification

Antibody–drug conjugates (ADCs) and proteolysis-targeting chimeras (PROTACs) deliver real but incomplete clinical benefit, limited by restricted penetration into tumour cores, efflux-mediated resistance, and outgrowth of microenvironmentally protected subclones. We ask a purely quantitative question: what would a small-molecule agent have to achieve for complete eradication of a heterogeneous tumour to be dynamically possible at all? We formalise a hypothetical tetramodular architecture (targeting ligand, catalytic NQO1-activated ROS generator, P-glycoprotein inhibitor, E3-recruiting warhead) and embed it in a dimensionally consistent multi-scale model comprising full target-mediated drug disposition, a perfusion-limited tumour compartment, quasi-steady-state intracellular exposure under non-competitively inhibitable efflux with drug-induced transporter up-regulation, timescale-separated ROS kinetics, and a three-clone Gompertz system with an explicit extinction threshold.The central result is analytic rather than simulational. Clone i can be driven to extinction if and only if its attainable kill rate exceeds a₀rᵢln(b/Vext), which for the hypoxia-adapted clone equals 2.35 d⁻¹ under Gompertz growth. Mono-mechanism comparators calibrated to ADC- and PROTAC-like potency have saturating kill ceilings of 0.50 and 0.60 d⁻¹ and therefore cannot eradicate that clone at any dose—a structural, not a dosing, limitation under Gompertz dynamics. The modelled multi-modal agent reaches 7.21 d⁻¹, clearing the Gompertz criterion with a 3.1-fold margin, and requires a sustained intracellular free concentration above 8.7 μM.Every quantitative claim above, and every table and figure in this manuscript, was regenerated by directly executing the embedded code (Appendix A) rather than asserted; three findings that emerged only once the analysis was actually run materially qualify the headline result. (i) A properly executed global sensitivity analysis (Saltelli sampling, N=256, 3584 model evaluations, Sobol total-order indices on log-transformed burden) shows that the intrinsic tumour growth rate a₀ and the perfusion exchange rate kpt—not the NQO1/ROS module—dominate output variance (ST=0.68 and 0.46 respectively, versus 0.28 and 0.25 for [E]NQO1 and ROS50); the efflux-module parameters remain necessary (Section 6) yet contribute negligible variance (ST<0.001), so that part of the original conjecture survives. (ii) Properly calibrating the Logistic and von Bertalanffy growth laws to reproduce the same untreated trajectory as the Gompertz law (rather than reusing Gompertz rate constants unchanged) shows the eradication criterion is not robust to the growth law at all: under Logistic growth the critical rate collapses to 0.15–0.18 d⁻¹, so that even the ADC and PROTAC comparators would succeed; under von Bertalanffy growth it explodes to 68–91 d⁻¹, so that even the modelled agent (ceiling 9.0 d⁻¹) would fail. The choice of growth law, not any single kinetic parameter, is the dominant structural uncertainty in this framework. (iii) A correctly specified hybrid stochastic simulation (deterministic pharmacokinetics driving Poisson birth–death kinetics on clone cell counts) shows that reliable (≥95%) stochastic extinction is achieved below, not above, the deterministic all-clones-cleared dose (D≈18.5 μM versus D=20 μM); at the deterministic threshold dose itself, stochastic replicates clear in 100% of trials. This is the opposite of the common expectation that demographic noise erodes reliability, and follows from the absorbing extinction-threshold convention rather than from any error in the deterministic result.Uncertainty propagation across 512 Latin-hypercube draws over the same twelve parameters gives an eradication probability of 55.1% (95% CI 50.7–59.3%, Wilson score), with a median cumulative burden of 41.8 AU·d and a heavily right-skewed 95% interval of 11.9–3297 AU·d driven by joint draws of high growth rate and low dose/penetration. This is, if anything, a more sobering headline number than a simple point estimate would suggest.We further establish the theoretical foundations of the model by proving existence and uniqueness of solutions via Lipschitz conditions, performing a nondimensionalisation that isolates the governing dimensionless groups, and analysing the stability of the tumour-free and extinction equilibria via Jacobian eigenvalues. We prove structural identifiability of the parameters before evaluating practical identifiability on synthetic data, confirming that the ROS-pathway enzyme concentration is sharply identifiable while the intrinsic clone kill-rate constants are not. Finally, we translate the architecture to chronic viral reservoirs (HIV/HBV), deriving an analogous analytic decay criterion; under the (unvalidated) assumption of sustained saturating exposure the translated model predicts a 15.2 and 10.6 order-of-magnitude reservoir reduction over 120 days for the HIV- and HBV-parameterised cases respectively. The framework is offered not as evidence that such molecules work, but as a falsifiable specification of what they must achieve, together with the measurements that would refute it, and—after this revision—as an explicit demonstration of how sensitive that specification is to structural modelling choices that are easy to state but, as we show, are not interchangeable in practice. All code, including the model core and every statistical analysis reported above, is embedded and reproduces every number in this manuscript from the fixed random seed stated in Section 14.