arXiv subjects

Peter S. Kim

Publications and source records attributed to Peter S. Kim.

16 recordsLinked to original sources

arXiv2026

Why males compete rather than care, with an application to supplying collective goods

The question of why males invest more into competition than offspring care is an age-old problem in evolutionary biology. On one hand, paternal care could increase the fraction of offspring surviving to maturity. On the other hand, competition could increase the likelihood of more paternities and thus the relative number of offspring produced. While drivers of these behaviours are often intertwined with a wide range of other constraints, here we present a simple dynamic model to investigate the benefits of these two alternative fitness-enhancing pathways. Using this framework we evaluate the sensitivity of equilibrium dynamics to changes in payoffs for male allocation to mating versus parenting. Even with strong effects of care on offspring survivorship, small competitive benefits can outweigh benefits from care. We consider an application of the model that includes men's competition for hunting reputations where big game supplies a benefit to all, and find a frequency-dependent parameter region within which, depending on initial population proportions, either strategy may outperform the other. Results demonstrate that allocation to competition gives males greater fitness than offspring care for a range of circumstances that are dependent on life-history parameters and, for the large-game hunting application, frequency dependent. The greater the collective benefit, the more individuals can be selected to supply it.

q-bio.PE↗

arXiv2026

Optimisation of neoadjuvant pembrolizumab therapy for locally advanced MSI-H/dMMR colorectal cancer using data-driven delay integro-differential equations

Colorectal cancer (CRC) poses a major public health challenge due to its increasing prevalence, particularly among younger populations. Microsatellite instability-high (MSI-H) CRC and deficient mismatch repair (dMMR) CRC constitute 15% of all CRC and exhibit remarkable responsiveness to immunotherapy, especially with PD-1 inhibitors. Despite this, there is a significant need to optimise immunotherapeutic regimens to maximise clinical efficacy and patient quality of life. To address this, we employ a novel framework driven by delay integro-differential equations to model the interactions among cancer cells, immune cells, and immune checkpoints in locally advanced MSI-H/dMMR CRC (laMCRC). Several of these components are being modelled deterministically for the first time in cancer, paving the way for a deeper understanding of the complex underlying immune dynamics. We consider two compartments$\unicode{x2014}$the tumour site and the tumour-draining lymph node (TDLN)$\unicode{x2014}$taking into account phenomena such as DC migration, T cell proliferation, and CD8+ T cell exhaustion and reinvigoration. Parameter values and initial conditions are derived from experimental data, integrating various pharmacokinetic, bioanalytical, and radiographic studies, along with deconvolution of bulk RNA-sequencing data from the TCGA COADREAD and GSE26571 datasets. We finally optimised neoadjuvant treatment with pembrolizumab, a widely used PD-1 inhibitor, to balance efficacy, efficiency, and toxicity in laMCRC patients. We mechanistically analysed factors influencing treatment success and improved upon currently FDA-approved therapeutic regimens for metastatic MSI-H/dMMR CRC, demonstrating that a single medium-to-high dose of pembrolizumab may be sufficient for effective tumour eradication while being efficient, safe, and practical.

q-bio.CB↗

arXiv2026

Sensitivity analysis-guided model reduction of a mathematical model of pembrolizumab therapy for de novo metastatic MSI-H/dMMR colorectal cancer

Colorectal cancer (CRC) is the third most commonly diagnosed cancer worldwide and the leading cause of cancer-related deaths in adults under 55, involving a complex interplay of biological processes such as dendritic cell (DC) maturation and migration, T cell activation and proliferation, cytokine production, and T cell and natural killer (NK) cell-mediated cancer cell killing. Microsatellite instability-high (MSI-H) CRC and deficient mismatch repair (dMMR) CRC constitute 15% of all CRC and 4% of metastatic CRC, and exhibit remarkable responsiveness to immunotherapy, especially with PD-1 inhibitors such as pembrolizumab. Mathematical models of the underlying immunobiology and the interactions underpinning immune checkpoint blockade offer mechanistic insights into tumour--immune dynamics and provide avenues for treatment optimisation and the identification of novel therapeutic targets. We used our data-driven model of de novo metastatic MSI-H/dMMR CRC (dnmMCRC) and performed sensitivity analysis-guided model reduction using the Fourier amplitude sensitivity testing (FAST) and extended FAST (EFAST) methods. In this work, we constructed two simplified models of dnmMCRC: one that faithfully reproduces all of the original model's trajectories, and a second, minimal model that accurately replicates the original dynamics while being highly extensible for future inclusion of additional components to explore various aspects of the anti-tumour immune response. Together, these resulting models offer a tractable foundation for future theoretical and computational studies of immune checkpoint blockade, avoiding unnecessary complexity while preserving mechanistic interpretability.

q-bio.QM↗

arXiv2026

Spatial dynamic modelling to understand how dendritic cell clustering affects T cell activation

The coordination of the immune system and its components is essential for the body to maintain a healthy status. Recent clinical studies show that breast cancer patients with high Dendritic cell clustering in tumour draining lymph nodes have improved survival outcomes, compared to those with a lower degree of clustering. These results suggest that a specific form of Dendritic cell clustering promotes T cell activation. However, the mechanistic effects of this spatial organisation is unclear. We develop a spatially dynamic model of T cells interacting with Dendritic cells within the lymph node. We present a novel probabilistic agent-based model (ABM) of T cells, and use it to derive the deterministic, phenotypically structured partial differential equation (PS-PDE) of T cell activation and motion. Using the PS-PDE, we derive analytic approximations of the expected T cell stimulation distribution, based on the topology and level of clustering of a given Dendritic cell population. Our analytic approximation enables us to identify T cell characteristics that benefit most from Dendritic cell clustering, to result in an enhanced stimulation distribution. We also perform a sensitivity analysis with our models to identify T cell characteristics that result in desirable T cell activation characteristics, such as rapid T cell activation, and robust heterogeneous T cell activation. Our key findings show that T cells with an intermediate level of stimulation uptake benefit most from higher levels of Dendritic cell clustering, activating with a comparable or greater abundance, and greater heterogeneity, when compared to T cells of a similar characteristic but with a lower level of Dendritic cell clustering.

q-bio.CB↗

arXiv2021

The role of antigen-competitive dynamics in regulating the immune response

The clonal expansion of T cells during an infection is tightly regulated to ensure an appropriate immune response against invading pathogens. Although experiments have mapped the trajectory from expansion to contraction, the interplay between mechanisms that control this response are not fully understood. Based on experimental data, we propose a model in which the dynamics of CD4+ T cell expansion is controlled through the interactions between T cells and antigen-presenting cells, where T cell stimulation is proportional to antigen availability and antigen availability is regulated through downregulation of antigen by T cells. This antigen-dependent-feedback mechanism operates alongside an intrinsic reduction in cell proliferation rate that may also be responsible for slowing expansion. Our model can successfully predict T cell recruitment rates into division, expansion and clonal burst size per cell when initial precursors are varied or when T cells are introduced late into an ongoing immune response. Importantly, the findings demonstrate that a feedback mechanism between T cells and antigen presenting cells, along with a reduction in cell proliferation rate, can explain the ability of the immune system to adapt its response to variations in initial conditions or changes that occur later in the response, ensuring a robust yet controlled line of defence against pathogens.

math.DS↗

arXiv2021

The role of viral infectivity in oncolytic virotherapy outcomes: A mathematical study

A model capturing the dynamics between virus and tumour cells in the context of oncolytic virotherapy is presented and analysed. The ability of the virus to be internalised by uninfected cells is described by an infectivity parameter, which is inferred from available experimental data. The parameter is also able to describe the effects of changes in the tumour environment that affect viral uptake from tumour cells. Results show that when a virus is inoculated inside a growing tumour, strategies for enhancing infectivity do not lead to a complete eradication of the tumour. Within typical times of experiments and treatments, we observe the onset of oscillations, which always prevent a full destruction of the tumour mass. These findings are in good agreement with available laboratory results. Further analysis shows why a fully successful therapy cannot exist for the proposed model and that care must be taken when designing and engineering viral vectors with enhanced features. In particular, bifurcation analysis reveals that creating longer lasting virus particles or using strategies for reducing infected cell lifespan can cause unexpected and unwanted surges in the overall tumour load over time. Our findings suggest that virotherapy alone seems unlikely to be effective in clinical settings unless adjuvant strategies are included.

math.DS↗

arXiv2021

Mathematical model for delayed responses in immune checkpoint blockades

We introduce a set of ordinary differential equations (ODE) that qualitatively reproduces delayed responses observed in immune checkpoint blockade therapy (e.g. anti-CTLA-4 Ipilimumab). This type of immunotherapy has been at the forefront of novel and promising cancer treatments over the past decade and was recognised by the 2018 Nobel Prize in Medicine. Our model describes the competition between effector T cells and non-effector T cells in a tumour. By calibrating a small subset of parameters that control immune checkpoint expression along with the patient's immune-system cancer readiness, our model is able to simulate either a complete absence of patient response to treatment, a quick anti-tumour T cell response (within days) or a delayed response (within months). Notably, the parameter space that generates a delayed response is thin and must be carefully calibrated, reflecting the observation that a small subset of patients experience such reactions to checkpoint blockade therapies. Finally, simulations predict that the anti-tumour T cell storm that breaks the delay is very short-lived compared to the length of time the cancer is able to stay suppressed. This suggests the tumour may subsist off an environment hostile to effector T cells; however, these cells are -- at rare times -- able to break through the tumour immunosuppressive defences to neutralise the tumour for a prolonged period. Our simulations aim to qualitatively describe the delayed response phenomenon without making precise fits to particular datasets, which are limited. It is our hope that our foundational model will stimulate further interest within the immunology modelling field.

math.DS↗

arXiv2021

Oncolytic virotherapy for tumours following a Gompertz growth law

We present a mathematical model describing oncolytic virotherapy treatment of a tumour that proliferates according to a Gompertz growth function. We present local stability analysis and bifurcation plots for relevant model parameters to investigate the typical dynamical regimes that the model allows. The model shows a singular equilibrium and a number of nonlinear behaviours that have interesting biological consequences, such as long-period oscillations and bistable states where two different outcomes can occur depending on the initial conditions. Complete tumour eradication appears to be possible only for parameter combinations where viral characteristics match well with the tumour growth rate. Interestingly, the model shows that therapies with a high initial injection or involving a highly infective virus do not universally result in successful strategies for eradication. Further, the use of additional, boosting injection schedules does not always lead to complete eradication. Our framework, instead, suggests that low viral loads can be in some cases more effective than high loads, and that a less resilient virus can help avoid high amplitude oscillations between tumours and virus. Finally, the model points to a number of interesting findings regarding the role of oscillations and bistable states between a tumour and an oncolytic virus. Strategies for the elimination of such fluctuations depend strongly on the initial viral load and the combination of parameters describing the features of the tumour and virus.

math.DS↗

arXiv2021

Effects of mutations and immunogenicity on outcomes of anti-cancer therapies for secondary lesions

Cancer development is driven by mutations and selective forces, including the action of the immune system and interspecific competition. When administered to patients, anti-cancer therapies affect the development and dynamics of tumours, possibly with various degrees of resistance due to immunoediting and microenvironment. Tumours are able to express a variety of competing phenotypes with different attributes and thus respond differently to various anti-cancer therapies. In this paper, a mathematical framework incorporating a system of delay differential equations for the immune system activation cycle and an agent-based approach for tumour-immune interaction is presented. The focus is on those metastatic, secondary solid lesions that are still undetected and non-vascularised. By using available experimental data, we analyse the effects of combination therapies on these lesions and investigate the role of mutations on the rates of success of common treatments. Findings show that mutations, growth properties and immunoediting influence therapies' outcomes in nonlinear and complex ways, affecting cancer lesion morphologies, phenotypical compositions and overall proliferation patterns. Cascade effects on final outcomes for secondary lesions are also investigated, showing that actions on primary lesions could sometimes result in unexpected clearances of secondary tumours. This outcome is strongly dependent on the clonal composition of the primary and secondary masses and is shown to allow, in some cases, the control of the disease for years.

math.DS↗

arXiv2019

Mathematical modelling of the interaction between cancer cells and an oncolytic virus: insights into the effects of treatment protocols

Oncolytic virotherapy is an experimental cancer treatment that uses genetically engineered viruses to target and kill cancer cells. One major limitation of this treatment is that virus particles are rapidly cleared by the immune system, preventing them from arriving at the tumour site. To improve virus survival and infectivity modified virus particles with the polymer polyethylene glycol (PEG) and the monoclonal antibody herceptin. While PEG modification appeared to improve plasma retention and initial infectivity it also increased the virus particle arrival time. We derive a mathematical model that describes the interaction between tumour cells and an oncolytic virus. We tune our model to represent the experimental data by Kim et al. (2011) and obtain optimised parameters. Our model provides a platform from which predictions may be made about the response of cancer growth to other treatment protocols beyond those in the experiments. Through model simulations we find that the treatment protocol affects the outcome dramatically. We quantify the effects of dosage strategy as a function of tumour cell replication and tumour carrying capacity on the outcome of oncolytic virotherapy as a treatment. The relative significance of the modification of the virus and the crucial role it plays in optimising treatment efficacy is explored.

q-bio.CB↗

arXiv2019

Influence of a mortality trade-off on the spreading rate of cane toads fronts

In this paper, we study the influence of the mortality trade-off in a nonlocal reaction-diffusion-mutation equation that we introduce to model the invasion of cane toads in Australia. This model is built off of one that has attracted attention recently, in which the population of toads is structured by a phenotypical trait that governs the spatial diffusion. We are concerned with the case when the diffusivity can take unbounded values and the mortality trade-off depends only on the trait variable. Depending on the rate of increase of the penalization term, we obtain the rate of spreading of the population. We identify two regimes, an acceleration regime when the penalization is weak and a linear spreading regime when the penalization is strong. While the development of the model comes from biological principles, the bulk of the article is dedicated to the mathematical analysis of the model, which is very technical.

math.AP↗

arXiv2019

Evolution of longevity, age at last birth and sexual conflict with grandmothering

We use a two-sex partial differential equation (PDE) model based on the Grandmother Hypothesis. We build on an earlier model by Kim et al. [27] by allowing for evolution in both longevity and age at last birth, and also assuming that post-fertile females support only their daughters' fertility. Similarly to Kim et al. [27], we find that only two locally stable equilibria exist: one corresponding to great ape-like longevities and the other corresponding to hunter-gatherer longevities. Our results show that grandmothering enables the transition between these two equilibria, without extending the end of fertility. Moreover, sensitivity analyses of the model show that male competition, arising from a skew in the mating sex ratio towards males, plays a significant role in determining whether the transition from great ape-like longevities to higher longevities is possible and the equilibrium value of the average adult lifespan. Whereas grandmothering effects have a significant impact on the equilibrium value of the average age at last birth and enable the transition to higher longevities, they have an insignificant impact on the equilibrium value of the average adult lifespan.

q-bio.PE↗

arXiv2019

Why does women's fertility end in mid-life? Grandmothering and age at last birth

Great apes, the other living members of our hominid family, become decrepit before the age of forty and rarely outlive their fertile years. In contrast, women - even in high mortality hunter-gatherer populations - usually remain healthy and productive well beyond menopause. The grandmother hypothesis aims to account for the evolution of this distinctive feature of human life history. Our previous mathematical simulations of that hypothesis fixed the end of female fertility at the age of 45, based on the similarities among living hominids, and then modeled the evolution of human-like longevity from an ancestral state, like that of the great apes, due only to grandmother effects. A major modification here allows the age female fertility ends to vary as well, directly addressing a version of the question, influentially posed by GC Williams six decades ago: Why isn't menopause later in humans? Our model is an agent-based model (ABM) that accounts for the coevolution of both expected adult lifespan and end of female fertility as selection maximizes reproductive value. We find that grandmother effects not only drive the population from an equilibrium representing a great ape-like longevity to a new human-like longevity, they also maintain the observed termination of women's fertility before the age of 50.

q-bio.PE↗

arXiv2019

Mentoring Undergraduate Interdisciplinary Mathematics Research Students: Junior Faculty Experiences

To be successful, junior faculty must properly manage their time in the face of expanding responsibilities. One such responsibility is supervising undergraduate research projects. Student research projects (either single or multi-student) can be undertaken as a full-time summer experience, or as a part-time academic year commitment. With many potential undergraduate research formats, and with different types of students, junior faculty may find challenges in forming their research group, establishing a structure that promotes student productivity, picking an appropriate project, or in effectively mentoring their students. This article draws from the authors' experiences to help junior faculty navigate these complexities so that all parties reap the benefits of undergraduate research in interdisciplinary mathematical disciplines.

math.HO↗

arXiv2016

Stability of travelling waves in a Wolbachia invasion

Numerous studies have examined the growth dynamics of Wolbachia within populations and the resultant rate of spatial spread. This spread is typically characterised as a travelling wave with bistable local growth dynamics due to a strong Allee effect generated from cytoplasmic incompatibility. While this rate of spread has been calculated from numerical solutions of reaction-diffusion models, none have examined the spectral stability of such travelling wave solutions. In this study we analyse the stability of a travelling wave solution generated by the reaction-diffusion model of Chan & Kim (2013) by computing the essential and point spectrum of the linearised operator arising in the model. The point spectrum is computed via an Evans function using the compound matrix method, whereby we find that it has no roots with positive real part. Moreover, the essential spectrum lies strictly in the left half plane. Thus, we find that the travelling wave solution found by Chan & Kim (2013) corresponding to competition between Wolbachia-infected and -uninfected mosquitoes is linearly stable. We employ a dimension counting argument to suggest that, under realistic conditions, the wavespeed corresponding to such a solution is unique.

math.DS↗

arXiv2009

Stability Analysis of a Simplified Yet Complete Model for Chronic Myelegenous Leukemia

We analyze the asymptotic behavior of a partial differential equation (PDE) model for hematopoiesis. This PDE model is derived from the original agent-based model formulated by (Roeder et al., Nat. Med., 2006), and it describes the progression of blood cell development from the stem cell to the terminally differentiated state. To conduct our analysis, we start with the PDE model of (Kim et al, JTB, 2007), which coincides very well with the simulation results obtained by Roeder et al. We simplify the PDE model to make it amenable to analysis and justify our approximations using numerical simulations. An analysis of the simplified PDE model proves to exhibit very similar properties to those of the original agent-based model, even if for slightly different parameters. Hence, the simplified model is of value in understanding the dynamics of hematopoiesis and of chronic myelogenous leukemia, and it presents the advantage of having fewer parameters, which makes comparison with both experimental data and alternative models much easier.

math.AP↗