Mathematical Biosciences最新文献

We consider an SEIR epidemic model on a network also allowing random contacts, where recovered individuals could either recover naturally or be diagnosed. Upon diagnosis, manual contact tracing is triggered such that each infected network contact is reported, tested and isolated with some probability and after a random delay. Additionally, digital tracing (based on a tracing app) is triggered if the diagnosed individual is an app-user, and then all of its app-using infectees are immediately notified and isolated. The early phase of the epidemic with manual and/or digital tracing is approximated by different multi-type branching processes, and three respective reproduction numbers are derived. The effectiveness of both contact tracing mechanisms is numerically quantified through the reduction of the reproduction number. This shows that app-using fraction plays an essential role in the overall effectiveness of contact tracing. The relative effectiveness of manual tracing compared to digital tracing increases if: more of the transmission occurs on the network, when the tracing delay is shortened, and when the network degree distribution is heavy-tailed. For realistic values, the combined tracing case can reduce $R_0$ by 20%–30%, so other preventive measures are needed to reduce the reproduction number down to 1.2–1.4 for contact tracing to make it successful in avoiding big outbreaks.

Recent studies have utilized evolutionary mechanisms to impede the emergence of drug-resistant populations. In this paper, we develop a mathematical model that integrates hormonal treatment, immunotherapy, and the interactions among three cell types: drug-sensitive cancer cells, drug-resistant cancer cells and immune effector cells. Dynamical analysis is performed, examining the existence and stability of equilibria, thereby confirming the model’s interpretability. Model parameters are calibrated using available prostate cancer data and literature. Through bifurcation analysis for drug sensitivity under different immune effector cells recruitment responses, we find that resistant cancer cells grow rapidly under weak recruitment response, maintain at a low level under strong recruitment response, and both may occur under moderate recruitment response. To quantify the competitiveness of sensitive and resistant cells, we introduce the comprehensive measures $R_1$ and $R_2$, respectively, which determine the outcome of competition. Additionally, we introduce the quantitative indicators $CI{E}_1$ and $CI{E}_2$ as comprehensive measures of the immune effects on sensitive and resistant cancer cells, respectively. These two indicators determine whether the corresponding cancer cells can maintain at a low level. Our work shows that the immune system is an important factor affecting the evolution of drug resistance and provides insights into how to enhance immune response to control resistance.

A fundamental feature of collective cell migration is phenotypic heterogeneity which, for example, influences tumour progression and relapse. While current mathematical models often consider discrete phenotypic structuring of the cell population, in-line with the ‘go-or-grow’ hypothesis (Hatzikirou et al., 2012; Stepien et al., 2018), they regularly overlook the role that the environment may play in determining the cells’ phenotype during migration. Comparing a previously studied volume-filling model for a homogeneous population of generalist cells that can proliferate, move and degrade extracellular matrix (ECM) (Crossley et al., 2023) to a novel model for a heterogeneous population comprising two distinct sub-populations of specialist cells that can either move and degrade ECM or proliferate, this study explores how different hypothetical phenotypic switching mechanisms affect the speed and structure of the invading cell populations. Through a continuum model derived from its individual-based counterpart, insights into the influence of the ECM and the impact of phenotypic switching on migrating cell populations emerge. Notably, specialist cell populations that cannot switch phenotype show reduced invasiveness compared to generalist cell populations, while implementing different forms of switching significantly alters the structure of migrating cell fronts. This key result suggests that the structure of an invading cell population could be used to infer the underlying mechanisms governing phenotypic switching.

We consider two types of models of regulatory network dynamics: Boolean maps and systems of switching ordinary differential equations. Our goal is to construct all models in each category that are compatible with the directed signed graph that describe the network interactions. This leads to consideration of lattice of monotone Boolean functions (MBF), poset of non-degenerate MBFs, and a lattice of chains in these sets. We describe explicit inductive construction of these posets where the induction is on the number of inputs in MBF.

Our results allow enumeration of potential dynamic behavior of the network for both model types, subject to practical limitation imposed by the size of the lattice of MBFs described by the Dedekind number.

Chronic pain is a major cause of disability and suffering in osteoarthritis (OA) patients. Endogenous specialised pro-resolving molecules (SPMs) curtail pro-inflammatory responses. One of the SPM intermediate oxylipins, 17-hydroxydocasahexaenoic acid (17-HDHA, a metabolite of docosahexaenoic acid (DHA)), is significantly associated with OA pain. The aim of this multidisciplinary work is to develop a mathematical model to describe the contributions of enzymatic pathways (and the genes that encode them) to the metabolism of DHA by monocytes and to the levels of the down-stream metabolites, 17-HDHA and 14-hydroxydocasahexaenoic acid (14-HDHA), motivated by novel clinical data from a study involving 30 participants with OA. The data include measurements of oxylipin levels, mRNA levels, measures of OA severity and self-reported pain scores.

We propose a system of ordinary differential equations to characterise associations between the different datasets, in order to determine the homeostatic concentrations of DHA, 17-HDHA and 14-HDHA, dependent upon the gene expression of the associated metabolic enzymes. Using parameter-fitting methods, local sensitivity and uncertainty analysis, the model is shown to fit well qualitatively to experimental data.

The model suggests that up-regulation of some ALOX genes may lead to the down-regulation of 17-HDHA and that dosing with 17-HDHA increases the production of resolvins, which helps to down-regulate the inflammatory response. More generally, we explore the challenges and limitations of modelling real data, in particular individual variability, and also discuss the value of gathering additional experimental data motivated by the modelling insights.

Blood coagulation is a network of biochemical reactions wherein dozens of proteins act collectively to initiate a rapid clotting response. Coagulation reactions are lipid-surface dependent, and this dependence is thought to help localize coagulation to the site of injury and enhance the association between reactants. Current mathematical models of coagulation either do not consider lipid as a variable or do not agree with experiments where lipid concentrations were varied. Since there is no analytic rate law that depends on lipid, only apparent rate constants can be derived from enzyme kinetic experiments. We developed a new mathematical framework for modeling enzymes reactions in the presence of lipid vesicles. Here the concentrations are such that only a fraction of the vesicles harbor bound enzymes and the rest remain empty. We call the lipid vesicles with and without enzyme TF:VIIa${}^{+}$ and TF:VIIa${}^{-}$ lipid, respectively. Since substrate binds to both TF:VIIa${}^{+}$ and TF:VIIa${}^{-}$ lipid, our model shows that excess empty lipid acts as a strong sink for substrate. We used our framework to derive an analytic rate equation and performed constrained optimization to estimate a single, global set of intrinsic rates for the enzyme–substrate pair. Results agree with experiments and reveal a critical lipid concentration where the conversion rate of the substrate is maximized, a phenomenon known as the template effect. Next, we included product inhibition of the enzyme and derived the corresponding rate equations, which enables kinetic studies of more complex reactions. Our combined experimental and mathematical study provides a general framework for uncovering the mechanisms by which lipid mediated reactions impact coagulation processes.

In addition to the traditional transmission route via the biting-and-defecating process, non-human host predation of triatomines is recognized as another significant avenue for Chagas disease transmission. In this paper, we develop an eco-epidemiological model to investigate the impact of predation on the disease’s spread. Two critical thresholds, $R_v^p$ (the basic reproduction number of triatomines) and $R_0^p$ (the basic reproduction number of the Chagas parasite), are derived to delineate the model’s dynamics. Through the construction of appropriate Lyapunov functions and the application of the Bendixson–Dulac theorem, the global asymptotic stabilities of the equilibria are fully established. The vector-free equilibrium $E_0$ is globally stable when $R_v^p<1$. $E_1$, the disease-free equilibrium, is globally stable when $R_v^p>1$ and $R_0^p<1$, while the endemic equilibrium $E^{\ast }$ is globally stable when both $R_v^p>1$ and $R_0^p>1$. Numerical simulations highlight that the degree of host predation on triatomines, influenced by non-human hosts activities, can variably increase or decrease the Chagas disease transmission risk. Specifically, low or high levels of host predation can reduce $R_0^p$ to below unity, while intermediate levels may increase the infected host populations, albeit with a reduction in $R_0^p$. These findings highlight the role played by non-human hosts and offer crucial insights for the prevention and control of Chagas disease.

This systematic review, conducted following the PRISMA guidelines, scrutinizes mathematical models employed in the study of Lassa fever. The analysis revealed the inherent heterogeneity in both models and data, posing significant challenges to parameter estimation. While health and behavioral interventions exhibit promise in mitigating the disease’s spread, their efficacy is contingent upon contextual factors. Identified through this review are critical gaps, limitations, and avenues for future research, necessitating increased harmonization and standardization in modeling approaches. The considerations of seasonal and spatial variations emerge as crucial elements demanding targeted investigation. The perpetual threat of emerging diseases, coupled with the enduring public health impact of Lassa fever, underscores the imperative for sustained research endeavors and investments in mathematical modeling. The conclusion underscored that while mathematical modeling remains an invaluable tool in the combat against Lassa fever, its optimal utilization mandates multidisciplinary collaboration, refined data collection methodologies, and an enriched understanding of the intricate disease dynamics. This comprehensive approach is essential for effectively reducing the burden of Lassa fever and safeguarding the health of vulnerable populations.

We consider compartmental models of communicable disease with uncertain contact rates. Stochastic fluctuations are often added to the contact rate to account for uncertainties. White noise, which is the typical choice for the fluctuations, leads to significant underestimation of the disease severity. Here, starting from reasonable assumptions on the social behavior of individuals, we model the contacts as a Markov process which takes into account the temporal correlations present in human social activities. Consequently, we show that the mean-reverting Ornstein–Uhlenbeck (OU) process is the correct model for the stochastic contact rate. We demonstrate the implication of our model on two examples: a Susceptibles–Infected–Susceptibles (SIS) model and a Susceptibles–Exposed–Infected–Removed (SEIR) model of the COVID-19 pandemic and compare the results to the available US data from the Johns Hopkins University database. In particular, we observe that both compartmental models with white noise uncertainties undergo transitions that lead to the systematic underestimation of the spread of the disease. In contrast, modeling the contact rate with the OU process significantly hinders such unrealistic noise-induced transitions. For the SIS model, we derive its stationary probability density analytically, for both white and correlated noise. This allows us to give a complete description of the model’s asymptotic behavior as a function of its bifurcation parameters, i.e., the basic reproduction number, noise intensity, and correlation time. For the SEIR model, where the probability density is not available in closed form, we study the transitions using Monte Carlo simulations. Our modeling approach can be used to quantify uncertain parameters in a broad range of biological systems.

Reaction–diffusion equations serve as fundamental tools in describing pattern formation in biology. In these models, nonuniform steady states often represent stationary spatial patterns. Notably, these steady states are not unique, and unveiling them mathematically presents challenges. In this paper, we introduce a framework based on bifurcation theory to address pattern formation problems, specifically examining whether nonuniform steady states can bifurcate from trivial ones. Furthermore, we employ linear stability analysis to investigate the stability of the trivial steady-state solutions. We apply the method to two classic reaction–diffusion models: the Schnakenberg model and the Gray–Scott model. For both models, our approach effectively reveals many nonuniform steady states and assesses the stability of the trivial solution. Numerical computations are also presented to validate the solution structures for these models.