Towards clinical translation of cancer nanomedicine, it is important to systematically investigate the various parameters related to nanoparticle (NP) physicochemical properties, tumor characteristics, and inter-individual variability that affect the tumor delivery efficiency of therapeutic nanomaterials. Comprehensive investigation of these parameters using traditional experimental approaches is impractical due to the vast parameter space; mathematical models provide a more tractable approach to navigate through such a multidimensional space. To this end, we have developed a predictive mathematical model of whole-body NP pharmacokinetics and their tumor delivery in vivo, and have conducted local and global sensitivity analyses to identify the factors that result in low tumor delivery efficiency and high off-target accumulation of NPs. Our analyses reveal that NP degradation rate, tumor blood viscosity, NP size, tumor vascular fraction, and tumor vascular porosity are the key parameters in governing NP kinetics in the tumor interstitium. The impact of these parameters on tumor delivery efficiency of NPs is discussed, and optimal values for maximizing NP delivery are presented.

In this work, we present a finite-difference scheme that preserves the non-negativity and the boundedness of some solutions of a FitzHugh–Nagumo equation. The method is explicit, and it approximates the solutions of the nonlinear, parabolic partial differential equation under study with a consistency of order 𝒪 (Δ t+(Δ x)²) in the Dirichlet regime investigated. We give sufficient conditions in terms of the computational and the model parameters, in order to guarantee the non-negativity and the boundedness of the approximations. We also provide analyses of consistency, linear stability and convergence of the method. Our simulations establish that the properties of non-negativity and boundedness are actually preserved by the scheme when the proposed constraints are satisfied. Finally, a comparison against some second-order accurate methods reveals that our technique is easier to implement computationally, and it is better at preserving the properties of non-negativity and boundedness of the solutions of the FitzHugh–Nagumo equation under study.

While the development of different vaccines slowed the dissemination of SARS-CoV-2, the occurrence of breakthrough infections has continued to fuel the COVID-19 pandemic. To secure at least partial protection in the majority of the population through 1 dose of a COVID-19 vaccine, delayed administration of boosters has been implemented in many countries. However, waning immunity and emergence of new variants of SARS-CoV-2 suggest that such measures may induce breakthrough infections due to intermittent lapses in protection. Optimizing vaccine dosing schedules to ensure prolonged continuity in protection could thus help control the pandemic. We developed a mechanistic model of immune response to vaccines as an in silico tool for dosing schedule optimization. The model was calibrated with clinical data sets of acquired immunity to COVID-19 mRNA vaccines in healthy and immunocompromised participants and showed robust validation by accurately predicting neutralizing antibody kinetics in response to multiple doses of COVID-19 mRNA vaccines. Importantly, by estimating population vulnerability to breakthrough infections, we predicted tailored vaccination dosing schedules to minimize breakthrough infections, especially for immunocompromised individuals. We identified that the optimal vaccination schedules vary from CDC-recommended dosing, suggesting that the model is a valuable tool to optimize vaccine efficacy outcomes during future outbreaks.