Mathematical Biosciences and Engineering最新文献

Cancer is a disease that arises from the uncontrolled growth of abnormal (tumor) cells in an organ and their subsequent spread into other parts of the body. If tumor cells spread to surrounding tissues or other organs, then the disease is life-threatening due to limited treatment options. This work applies an agent-based model to investigate the effect of intra-tumoral communication on tumor progression, plasticity, and invasion, with results suggesting that cell-cell and cell-extracellular matrix (ECM) interactions affect tumor cell behavior. Additionally, the model suggests that low initial healthy cell densities and ECM protein densities promote tumor progression, cell motility, and invasion. Furthermore, high ECM breakdown probabilities of tumor cells promote tumor invasion. Understanding the intra-tumoral communication under cellular stress can potentially lead to the design of successful treatment strategies for cancer.

A vegetation model composed of water and plants was proposed by introducing a weighted graph Laplacian operator into the reaction-diffusion dynamics. We showed the global existence and uniqueness of the solution via monotone iterative sequence. The parameter space of Turing patterns for plant behavior is obtained based on the analysis of the eigenvalues of the Laplacian of weighted graph, while the amplitude equation determining the stability of Turing patterns is obtained by weakly nonlinear analysis. We also show that the optimal rainfall is only determined by the density of the water. By some numerical simulations, we examine the individual effect of diffusion term on the formation of regular Turing patterns. We show that the large diffusion induces stable Turing patterns.

Mosquito-borne infectious diseases represent a significant public health issue. Age has been identified as a key risk factor for these diseases, and another phenomenon reported is relapse, which involves the reappearance of symptoms after a symptom-free period. Recent research indicates that susceptibility to and relapse of mosquito-borne diseases are frequently age-dependent. This paper proposes a new model to better capture the dynamics of mosquito-borne diseases by integrating two age-dependent factors: chronological age and asymptomatic-infection age. Chronological age refers to the time elapsed from the date of birth of the host to the present time. On the other hand, asymptomatic infection age denotes the time elapsed since the host became asymptomatic after the primary infection. The system of integro-differential equations uses flexible, unspecified functions to represent these dependencies, assuming they are integrable. We analyzed the global stability of both the disease-free and endemic equilibrium states using the direct Lyapunov method with Volterra-type Lyapunov functionals. Additionally, the paper explores several special cases involving well-known host-vector models.

This paper presents a mathematical model to describe the spread of flavescence dorée, a disease caused by the bacterium Candidatus Phytoplasma vitis, which is transmitted by the insect vector Scaphoideus titanus in grapevine crops. The key contribution of this work is the derivation of conditions under which positive periodic solutions exist. These conditions are based on the assumption that key factors such as recruitment rates, disease transmission, and vector infectivity vary periodically, thus reflecting seasonal changes. The existence of these periodic solutions is proven using the degree theory, and numerical examples are provided to support the theoretical findings. This model aims to enhance the understanding of the epidemiological dynamics of flavescence dorée and contribute to developing better control strategies to manage the disease in grapevines.

The invasive stink bug Halyomorpha halys has become an important pest of many crops, causing severe economic losses to farmers. Control of the pest mainly relies on multiple applications of broad-spectrum insecticides, undermining the integrated pest management programs and causing secondary pest outbreaks. In the native area, egg parasitoids are the main natural enemies of H. halys, among which Trissolcus japonicus is considered the predominant species. In Italy, adventive populations of T. japonicus and Trissolcus mitsukurii, another egg parasitoid of H. halys in Japan, have established themselves. These two species, together with the indigenous Anastatus bifasciatus, are capable of attacking the eggs of the exotic host. Focusing on the situation in Northern Italy, where also the hyperparasitoid Acroclisoides sinicus is present, a discrete-time model is developed for the simulation of the pest evolution. It is based on actual field data collected over a timespan of five years. The simulations indicate that egg parasitoid by themselves do not suppress populations to non-pest levels, but can play an important role in reducing their impact. Both the data from the five-year surveys and those available in the literature are used in the model. It has some limitations in the fact that climatic conditions were not considered, while more accurate simulations could be performed with additional collection of field data, which at the moment are based on partial field observations not sampled at the same sites.

The process of viral infection spreading in tissues was influenced by various factors, including virus replication within host cells, transportation, and the immune response. Reaction-diffusion systems provided a suitable framework for examining this process. In this work, we studied a nonlocal reaction-diffusion system of equations that modeled the distribution of viruses based on their genotypes and their interaction with the immune response. It was shown that the infection may persist at a certain level alongside a chronic immune response, exhibiting spatially uniform or oscillatory behavior. Finally, the immune cells may become entirely depleted, leading to a high viral load persisting in the tissue. Numerical simulations were employed to elucidate the nonlinear dynamics and pattern formation inherent in the nonlocal model.

In deciding whether to contribute to a public good, people often face a social dilemma known as the tragedy of the commons: either bear the cost of promoting the collective welfare, or free-ride on the efforts of others. Here, we study the dynamics of cooperation in the context of the threshold public goods games, in which groups must reach a cumulative target contribution to prevent a potential disaster, such as an environmental crisis or social unrest, that could result in the loss of all private wealth. The catch is that the crisis may never materialize, and the investment in the public good is lost. Overall, higher risk of loss promotes cooperation, while larger group size tends to undermine it. For most parameter settings, free-riders (defectors) cannot be eliminated from the population, leading to a coexistence equilibrium between cooperators and defectors for infinite populations. However, this equilibrium is unstable under the effect of demographic noise (finite population), since the cooperator-only and defector-only states are the only absorbing states of the stochastic dynamics. We use simulations and finite-size scaling to show that cooperators eventually die off and derive scaling laws for the transient lifetimes or half-lives of the coexistence metastable state. We find that for high risk, the half-life of cooperators increases exponentially with population size, while for low risk, it decreases exponentially with population size. At the risk threshold, where the coexistence regime appears in a discontinuous manner, the half-life increases with a power of the population size.

The incompatible insect technique based on Wolbachia is a promising alternative to control mosquito-borne diseases, such as dengue fever, malaria, and Zika, which drives wild female mosquitoes sterility through a mechanism cytoplasmic incompatibility. A successful control program should be able to withstand the perturbation induced by the immigration of fertilized females from surrounding uncontrolled areas. In this paper, we formulated a system of delay differential equations, including larval and adult stages, interfered by Wolbachia-infected males. We classified the release number of infected males and immigration number of fertile females, to ensure that the system displays globally asymptotically stable or bistable dynamics. The immigration of fertile females hinders the maximum possible suppression efficiency so that the wild adults cannot be reduced to a level below $ A^*_infty $. We identified the permitted most migration number to reduce the wild adults to a target level. To reduce up to $ 90% $ of wild adults in the peak season within two months, an economically viable strategy is to reduce the immigration number of wild females less than $ 0.21% $ of the carrying capacity of adults in the control area.

Identifying epidemic-driving factors through epidemiological modeling is a crucial public health strategy that has substantial policy implications for control and prevention initiatives. In this study, we employ dynamic modeling to investigate the transmission dynamics of pneumonic plague epidemics in Hong Kong from 1902 to 1904. Through the integration of human, flea, and rodent populations, we analyze the long-term changing trends and identify the epidemic-driving factors that influence pneumonic plague outbreaks. We examine the dynamics of the model and derive epidemic metrics, such as reproduction numbers, that are used to assess the effectiveness of intervention. By fitting our model to historical pneumonic plague data, we accurately capture the incidence curves observed during the epidemic periods, which reveals some crucial insights into the dynamics of pneumonic plague transmission by identifying the epidemic driving factors and quantities such as the lifespan of flea vectors, the rate of rodent spread, as well as demographic parameters. We emphasize that effective control measures must be prioritized for the elimination of fleas and rodent vectors to mitigate future plague outbreaks. These findings underscore the significance of proactive intervention strategies in managing infectious diseases and informing public health policies.