Bulletin of Mathematical Biology最新文献

In this paper we analyze the effect of substitution rate heterogeneity on the sample complexity of species tree estimation. We consider a model based on the multi-species coalescent (MSC), with the addition that gene trees exhibit random i.i.d. rates of substitution. Our first result is a lower bound on the number of loci needed to distinguish 2-leaf trees (i.e., pairwise distances) with high probability, when substitution rates satisfy a growth condition. In particular, we show that to distinguish two distances differing by length f with high probability, one requires $\Omega \left(f^{-2}\right)$ loci, a significantly higher bound than the constant rate case. The second main result is a lower bound on the amount of data needed to reconstruct a 3-leaf species tree with high probability, when mutation rates are gamma distributed. In this case as well, we show that the number of gene trees must grow as $\Omega \left(f^{-2}\right)$ .

This study investigates the use of the Sterile Insect Technique (SIT) combined with Entomopathogenic Fungi soil treatment (EPFS) to control two major pests: the Mediterranean fruit fly and the Oriental fruit fly. The SIT involves releasing sterile males to mate with wild females, but the challenge lies in female polyandry (re-mating) and residual fertility in sterile males. We develop a continuous release SIT model with single- and double-mated females, but with a novel approach to accounting the residual fertility parameter, $\epsilon$ . We also consider scenarios where the competitiveness of sterile males may decline between the first and the second mating. A key finding is that insect elimination, at least locally, with SIT can only occur when the product of the residual fertility parameter, $\epsilon$ , and the basic reproduction number of sterile mated females, $R_S$ , is less than 1. We also prove the existence of a sterile male release threshold, above which global elimination is possible. When $\epsilon R_S$ is greater than one, elimination is impossible regardless of the size of sterile male releases. We also extend our results to periodic releases. We illustrate our theoretical findings using numerical simulations, with parameters from the Mediterranean fruit fly (medfly), with and without ginger root oil (GRO) treatment, and the oriental fruit fly, with and without Methyl-Eugenol (ME) treatment. Both treatments are known to enhance sterile male competitiveness. We also show that combining SIT with EPFS can greatly improve SIT efficiency, and, in particular, reduce the constraint on residual fertility. We conclude that re-mating and residual fertility can have a significant impact on the effectiveness of SIT. However, this mainly depends on whether SIT is used in combination with EPFS or not, and also on the knowledge of the parameters of sterile-mated females which seem to have been superficially studied in many SIT programs so far.

We investigate the spatiotemporal dynamics of a non-local mussel-algae model, defined on a square domain with time delays and Neumann boundary conditions. Initially, we examine the well-posedness of the solutions. By analyzing the multiplicity of eigenvalues, we establish the existence of both Hopf and equivariant Hopf bifurcations. Using tools such as phase space decomposition, center manifold reduction, equivariant Hopf bifurcation theory, and the normal form method, we derive third-order truncated normal forms near the equivariant Hopf bifurcation point. This allows us to classify the system's spatiotemporal patterns into ten distinct types within the parameter plane. Unlike models constructed on one-dimensional domains, the two-dimensional symmetric model demonstrates more complex dynamic behaviors, including standing waves, rotating waves, stripes, and spots. Numerical simulations not only corroborate the theoretical predictions but also align with field observation in ecological systems, shedding light on the mechanisms underlying the formation of regular patterns due to the behavioral aggregation of mussels.

Human behavior plays a pivotal role in mitigating the global spread of infectious diseases, rendering it an indispensable characteristic of effective disease control efforts. While prior research has examined behavioral changes in disease control either through the force of infection or prevalence-based recruitment, the combined effects of these approaches remain largely unexplored. To bridge this gap, we develop a mathematical model that integrates behavioral modifications from both perspectives, with a focus on resource-limited settings-a critical factor for managing re-emerging diseases. Our analytical results indicate that disease dynamics are influenced not only by the basic reproduction number ( $R_0$ ) but also regulated by a threshold value ( $R_c$ ), which can lead to disease persistence through backward bifurcation. The model reveals a complex dynamic view, highlighting the intricate role of behavioral modifications in suppressing multiple waves of infection. To optimize behavioral strategies, we introduce a contour-area optimization method to identify the most effective responses. Using real-world data from the Monkeypox outbreaks in the United States of America. and the Democratic Republic of Congo (spanning January 7 to August 13, 2024), we estimated critical parameters for both regions. The results highlight a significant reduction in $R_0$ when behavioral interventions targeted both transmission pathways, compared to focusing solely on one. Furthermore, we provide short- and long-term forecasts of the effects of these interventions, offering actionable insights for resource-constrained countries. This research underscores the importance of behavioral adaptations in strengthening disease control measures and advancing sustainable public health efforts, even in regions with sparse resources.

Autonomous differential equation compartmental models hold broad utility in epidemiology and public health. However, these models typically cannot account explicitly for myriad factors that affect the trajectory of infectious diseases, with seasonal variations in host behavior and environmental conditions as noteworthy examples. Fortunately, using non-autonomous differential equation compartmental models can mitigate some of these deficiencies, as the inclusion of time-varying parameters can account for temporally varying factors. The inclusion of these temporally varying factors does come at a cost though, as many analysis techniques, such as the use of Poincaré maps and Floquet theory, on non-autonomous differential equation compartmental models are typically only tractable numerically. Here, we illustrate a rare $n$ -strain generalized Susceptible-Infectious-Susceptible (SIS) compartmental model, with a general time-varying recovery rate, which features Floquet exponents that are algebraic expressions. We completely characterize the persistence and stability properties of our $n$ -strain generalized SIS model for $n\ge 1$ . We also derive a closed-form solution in terms of elementary functions for the single-strain SIS model, which is capable of incorporating almost any infectious period distribution. Finally, to demonstrate the applicability of our work, we apply it to recent syphilis incidence data from the United States, utilizing Akaike Information Criteria and Forecast Skill Scores to inform on the model's goodness of fit relative to complexity and the model's capacity to predict future trends.

Host defense and pathogen virulence interact and mutually shape each other's evolution. Host-pathogen co-evolutionary outcomes have potentially significant impacts on population dynamics and vice versa. To investigate host-pathogen interactions and explore the impact of micro-level co-evolutionary outcomes on macro-level epidemics, we develop a co-evolutionary model with a combined host-defense strategy. Our results illustrate that host-pathogen co-evolution may induce infection cycling and lead to the vanishing of the disease-induced hydra effect, whereas pathogen mono-evolution strengthens the hydra effect in both range and magnitude. As the recovery rate increases, we find a counter-intuitive effect of increased disease prevalence due to host-pathogen co-evolution: the disease is first highly infectious and lethal, then highly infectious but with low lethality. Such diverse outcomes suggest that this combined co-evolutionary and epidemiological framework holds great promise for a better understanding of infection.

Adaptive therapy (AT) protocols have been introduced to combat drug resistance in cancer, and are characterized by breaks from maximum tolerated dose treatment (the current standard of care in most clinical settings). These breaks are scheduled to maintain tolerably high levels of tumor burden, employing competitive suppression of treatment-resistant sub-populations by treatment-sensitive sub-populations. AT has been integrated into several ongoing or planned clinical trials, including treatment of metastatic castrate-resistant prostate cancer, ovarian cancer, and BRAF-mutant melanoma, with initial clinical results suggesting that it can offer significant extensions in the time to progression over the standard of care. Prior AT protocols apply drug treatment when the tumor is within a specific size window, typically determined by the initial tumor size. However, this approach may be sub-optimal as it does not account for variation in tumor dynamics between patients, resulting in significant heterogeneity in patient outcomes. Mathematical modeling and analysis have been proposed to optimize adaptive protocols, but they do not account for clinical restrictions, most notably the discrete time intervals between the clinical appointments where a patient's tumor burden is measured and their treatment schedule is re-evaluated. We present a general framework for deriving optimal treatment protocols that account for these discrete time intervals, and derive optimal schedules for several models to avoid model-specific personalization. We identify a trade-off between the frequency of patient monitoring and the time to progression attainable, and propose an AT protocol that determines drug dosing based on a patient-specific threshold for tumor size. Finally, we identify a subset of patients with qualitatively different dynamics that instead require a novel AT protocol based on a threshold that changes over the course of treatment.

Tree balance plays an important role in various research areas in phylogenetics and computer science. Typically, it is measured with the help of a balance index or imbalance index. There are more than 25 such indices available, recently surveyed in a book by Fischer et al. They are used to rank rooted binary trees on a scale from the most balanced to the least balanced. We show that a wide range of subtree-size based measures satisfying concavity and monotonicity conditions are minimized by the complete or greedy from the bottom (GFB) tree and maximized by the caterpillar tree, yielding an infinitely large family of distinct new imbalance indices. Answering an open question from the literature, we show that one such established measure, the $\hat{s}$ -shape statistic, has the GFB tree as its unique minimizer. We also provide an alternative characterization of GFB trees, showing that they are equivalent to complete trees, which arise in different contexts. We give asymptotic bounds on the expected $\hat{s}$ -shape statistic under the uniform and Yule-Harding distributions of trees, and answer questions for the related Q-shape statistic as well.

Clonorchiasis is a foodborne disease caused by parasites and transmitted to humans through intermediate hosts. Clonorchis sinensis parasitizes in the bile ducts of human liver and causes organ lesions. The cercariae and metacercaria of Clonorchis sinensis have seasonal variations and may be affected by high water temperature in summer. We formulate a partial differential equations (PDE) model which incorporates seasonality, spatial heterogeneity and the extrinsic incubation period (EIP) of the parasite. We present the basic reproduction number $R_0$ and discuss the global dynamics of the model. Particularly, we choose parameters to fit the Clonorchiasis epidemic data in Guangxi, China. Our study indicates that the basic reproduction number of cases of clonorchiasis in Guangxi is $R_0$ =1.025 and the number of existing infection cases is still very large, if the prevention and control measures of Clonorchiasis are not strengthened.

We introduce two mathematical models for the spread of an SIR-type infectious disease, incorporating direct (person-to-person) and indirect (environment-to-person) transmissions, latent periods, asymptomatic infections, and different isolation rates for exposed, asymptomatic and symptomatic individuals. The first model employs the classical homogeneous mixing approach, while the second uses the edge-based compartmental approach to consider heterogeneity in the number of contacts within the population through a random contact network. Key epidemiological metrics, including the basic reproduction number and final epidemic size, are derived and illustrated through simulations for both models. Motivated by emerging infectious diseases with multiple transmission routes such as cholera and Mpox, we conduct sensitivity analyses to assess the impact of parameter variations and control measures. We also explore how secondary transmission routes influence disease spread and when the dominant route may switch over time. In this respect, our main theoretical results demonstrate that such a 'switching phenomenon' cannot occur in homogeneous mixing models or Poissonian networks when person-to-person transmission initially dominates, while numerical simulations show that it may occur in other networks such as scale-free and regular networks. These findings highlight the risks of designing public health interventions based solely on early disease dynamics and provide insights into controlling infections with multiple transmission routes.