Bulletin of Mathematical Biology最新文献

The 2009 influenza A (H1N1) epidemic in China provided a unique natural experiment to evaluate school closures, as it overlapped with two school vacations. Utilizing the epidemiological data from this outbreak, our study specifically assesses the impact of holidays and systematically evaluates the efficacy of school-specific prevention measures in curbing influenza transmission. By using the enhanced piecewise linear representation model and calculating the effective reproduction number R_t, we divided the entire pandemic period into six stages. We employed the Susceptible-Exposed-Infective-Removed model with quarantine compartments to align with the prevention and control policy. We quantified the effectiveness of holidays and school-specific prevention strategies using parameter estimation results. Moreover, we explored several comparative scenarios, including holiday cancellations or extensions, to further demonstrate the impact of school closure and policies. The comparison of different transmission phases revealed a 14.0% and 16.5% reduction in the mean of R_t during the summer vacation and the National Day holiday, respectively. Furthermore, the relaxation of school-specific preventive measures could potentially lead to a doubling of the accumulated case count within several months. In contrast, the extension of holiday periods demonstrated a notable mitigating impact on the epidemic curve. School-specific prevention strategies and school holidays exert a beneficial and significant influence on mitigating the spread of the influenza A (H1N1) epidemic. Our research findings and methods can provide insights for implementing school closure strategies to mitigate similar emerging infectious diseases.

Intestinal crypts are test tube-like structures lined with an epithelial monolayer. Under homeostasis, mitotic forces drive epithelial cells to migrate up the crypt, from the stem cell niche. As the cells migrate up the crypt, they differentiate into specialised cells. This process is regulated by morphogen gradients established by distinct populations of subepithelial fibroblasts, and recent studies suggest fibroblasts and epithelial cells have co-evolved to maintain crypt structure and function via complementary morphogen expression. We present a mathematical model of fibroblast-epithelial cross-talk, in which fibroblast and epithelial phenotypes emerge from morphogen binding to cell surface receptors. The model predicts the formation of distinct zones of mutually supporting phenotypes at different crypt heights. These findings support the idea that fibroblast and epithelial cell phenotypes are an emergent property of the crypt microenvironment. We use the model to investigate how mutations in the fibroblasts may disrupt these phenotypic zones. Our results suggest that such mutations may lead to uncontrolled epithelial cell growth and, as such, indicate how dysfunctional fibroblasts may contribute to the emergence of colorectal cancer.

Colorectal cancer (CRC) is the third most common malignancy worldwide, and accounts for approximately 10% of all cancers and an estimated 850,000 deaths annually. Within CRC, MSI-H/dMMR tumours are highly immunogenic due to their high mutational burden and neoantigen load, yet can evade immunosurveillance via PD-1/PD-L1-mediated signalling. Pembrolizumab, an anti-PD-1 antibody approved for unresectable or metastatic MSI-H/dMMR CRC, is emerging as a promising neoadjuvant option in the locally advanced setting, inducing rapid, deep and durable immune responses. In this work, we construct a minimal model of neoadjuvant pembrolizumab therapy in locally advanced MSI-H/dMMR CRC (laMCRC) using ordinary differential equations (ODEs), providing a highly extensible model that captures the main immune dynamics involved. On the other hand, agent-based models (ABMs) naturally capture stochasticity, interactions at an individual level, and discrete events that lie beyond the scope of differential-equation formulations. As such, we also convert our ODE model, with parameters calibrated to experimental data, to an ABM, preserving its dynamics while providing a flexible platform for future mechanistic investigation and modelling.

The purpose of this article is to identify the appropriate interface conditions to be coupled with phenotype-structured models, in which the motility terms depend on both cell density and phenotypic expression and where the cell population lives in a domain characterized by the presence of thin physical structures, such as basement membranes, vessel walls, and cell layers. A set of biophysically consistent transmission conditions is derived through an asymptotic method. The way in which they depend on the phenotype is found, determining the ability or inability of the cells to cross the membrane-like structure. In this way, the interface can act as a selector of more invasive phenotypes with respect to more residential ones. Numerical simulations confirm the analytical findings and provide additional insights into the influence of each model component. Overall, our results highlight how the interplay between phenotypic traits and migratory behaviour governs the spatial distribution of heterogeneous cell populations in the presence of physical interfaces, laying the groundwork for future theoretical and computational studies.

Parameter nonidentifiability is a critical challenge in infectious disease modeling, where infinitely many parameter values produce equally good fits to observed data but lead to significantly different future predictions. Many methods have been developed to address this issue, including mathematical analysis, computational techniques, and statistical approaches. While each provides valuable insights, the integration of computationally efficient identifiability analysis with Bayesian inference for practical parameter estimation has received relatively less attention. In this paper, we incorporate a sensitivity matrix based identifiability analysis into a Bayesian framework to assess parameter identifiability. By examining identifiability under prior distribution, we design Markov Chain Monte Carlo (MCMC) algorithms that integrate identifiability information to enhance the mixing and efficiency of the sampler. Posterior identifiability analysis can then be performed using the sampling results to assess the practical nonidentifiability of a model. By comparing the posterior nonidentifiability results across different models, our method enables principled model selection strategies that penalize nonidentifiable models within a rigorous Bayesian setting. Numerical studies confirm that widely used epidemic models such as SIR, SEIR, and SEIAR are often practically nonidentifiable when calibrated with limited data, underscoring the importance of model parsimony.

Accurate, decision-ready estimates of time-varying transmission rates are critical, yet thought to be sensitive to model specification. We test this sensitivity by applying a continuous inverse method to weekly influenza and measles data, comparing reconstructions across eight common compartmental structures (SIS/SIR/SEIS/SEIR and vaccinated variants) and across five incidence forms (mass action vs. saturated). Timing and ordering of peaks and troughs in the transmission rates are highly consistent across influenza models, with amplitude shifts matching mechanistic expectations (attenuation with vaccination; smoothing with latent periods). For measles, we show that the transmission rates under saturated incidence preserve the rise-and-fall ordering observed under mass action and provide a sufficient condition ensuring matched monotonicity. These results indicate inverse transmission rate reconstructions are robust to typical structural and incidence choices, supporting their routine use for interpreting transmission dynamics, short-term forecasting, and intervention assessment.

Gene duplication is a fundamental evolutionary mechanism that contributes to biological complexity and diversity (Fortna et al. 2004). Traditionally, research has focused on the duplication of gene sequences (Zhang 1914). However, evidence suggests that the duplication of regulatory elements may also play a significant role in the evolution of genomic functions (Teichmann and Babu 2004; Hallin and Landry 2019). In this work the evolution of regulatory relationships belonging to gene-specific-substructures in a GRN are modeled. In the model, a network grows from an initial configuration by repeatedly choosing a random gene to duplicate. The likelihood that the regulatory relationships associated with the selected gene are retained through duplication is determined by a vector of probabilities. That is to say that each gene family has its own probability of retaining regulatory relationships. Occurrences of gene-family-specific substructures are counted under the gene duplication model. In this work gene-family-specific substructures are referred to as subnetwork motifs. These subnetwork motifs are motivated by network motifs which are patterns of interconnections that recur more often in a specialized network than in a random network (Milo et al. 2002). Subnetwork motifs differ from network motifs in the way that subnetwork motifs are instances of gene-family-specific substructures while network motifs are isomorphic substructures. These subnetwork motifs are counted under Full and Partial Duplication, which differ in the way in which regulation relationships are inherited. Full duplication occurs when all regulatory links are inherited at each duplication step, and Partial Duplication occurs when regulation inheritance varies at each duplication step. Note that Full Duplication is just a special case of Partial Duplication. Moments for the number of occurrences of subnetwork motifs are determined in each model. In the end, the results presented offer a method for discovering gene-family-specific substructures that are significant in a GRN under gene duplication.

Disease X, a yet-to-be-identified pathogen of pandemic potential, underscores the urgency of proactive surveillance and preparedness. Developing prototype vaccine for representative pathogens is key to this effort. In alignment with the "100 Day Mission" to ensure equitable vaccine access, this study aims to identify desirable vaccine features needed to control future pathogens outbreaks, possibly SARS-CoV-2 type. We developed an individual-based transmission model integrating viral load and antibody kinetics to examine combinations of the virus's basic reproduction number (R₀) and vaccine characteristics, including (1) the concentration of antibodies required for 50% of the maximum protective effect (EC50), representing vaccine efficacy to limit infection, (2) the half-life of plasma-secreting cells associated with wanning immunity, and (3) the vaccine's impact on the virus's infection rate of target cells, representing vaccine's potency to limit transmission and severity. Their impacts on infections and hospitalizations were quantified over 18 months in a population of 10,000, with vaccination starting on Day 100 under random or age-prioritized allocation, without supply constraints. Vaccines with the same features as the BNT162b2 vaccine were estimated to avert 23-47% of cases and 32-61% of hospitalizations compared to no vaccine, with effect sizes declining as R₀ increased. Lowering EC50 or extending plasma-secreting cell half-life decreased transmission, although gains plateaued. Modifying the virus-target cell infection rate had minimal impact on population-level outcomes, and vaccine allocation strategy had limited impacts. Our findings suggest that vaccine development for future pandemics should prioritize improving EC50, followed by increasing a longer-term exposure.

It is often debated whether group selection can explain altruistic behaviors that lower the fitness of individual organisms for the benefit of their group. Several models of group selection are simulated here with more details and fewer simplifying assumptions than previous quantitative studies. The simulated models include island models with selective extinction, selective dispersal, selective migration, outsider exclusion, conformity, altruistic punishment, haystack model, and a new model with floating group territories. The simulations are repeated with different parameter sets in order to map the parameter areas that lead to either fixation of altruism, fixation of egoism, or stable polymorphism. This can help decide whether a particular behavior can be explained by genetic group selection. The conditions for group selection to override counteracting individual selection are found to be very restrictive. These conditions are met for eusocial insects, some parasites, and a few other species. The necessary conditions are unlikely to have been met in the evolutionary history of humans and most other group-living animals. Altruistic behaviors in humans could not have evolved without involving cultural mechanisms, including norms, rewards and punishments, reputation, and leadership. A comprehensive open-source simulation program is provided to facilitate further research.