Mathematical Biosciences最新文献

In this paper, we present a virus infection model that incorporates eclipse-stage and Beddington–DeAngelis function, along with perturbation in infection rate using logarithmic Ornstein–Uhlenbeck process. Rigorous analysis demonstrates that the stochastic model has a unique global solution. Through construction of appropriate Lyapunov functions and a compact set, combined with the strong law of numbers and Fatou’s lemma, we obtain the existence of the stationary distribution under a critical condition, which indicates the long-term persistence of T-cells and virions. Moreover, a precise probability density function is derived around the quasi-equilibrium of the model, and spectral radius analysis is employed to identify critical condition for elimination of the virus. Finally, numerical simulations are presented to validate theoretical results, and the impact of some key parameters such as the speed of reversion, volatility intensity and mean infection rate are investigated.

Plants in arid environments have evolved many strategies to resist drought. Among them, the developed water storage tissue is an essential characteristic of xerophytes. To clarify the role of water storage capacity in plant performance, we originally formulate a stoichiometric model to describe the interaction between plants and water with explicit water storage. Via an ecological reproductive index, we explore the effects of precipitation and water storage capacity on plant dynamics. The model possesses saddle–node bifurcation and forward or backward bifurcation, and the latter may lead to the emergence of alternative stable states between a stable survival state and a stable extinction state. Numerical simulations illustrate the persistence and resilience of plants regulated by soil conditions, precipitation and water storage capacity. Our findings contribute to the botanical theory in the perspectives of environmental change and plant water storage traits.

Oncologists and applied mathematicians are interested in understanding the dynamics of cancer-immune interactions, mainly due to the unpredictable nature of tumour cell proliferation. In this regard, mathematical modelling offers a promising approach to comprehend this potentially harmful aspect of cancer biology. This paper presents a novel dynamical model that incorporates the interactions between tumour cells, healthy tissue cells, and immune-stimulated cells when subjected to simultaneous chemotherapy and radiotherapy for treatment. We analysed the equilibria and investigated their local stability behaviour. We also study transcritical, saddle–node, and Hopf bifurcations analytically and numerically. We derive the stability and direction conditions for periodic solutions. We identify conditions that lead to chaotic dynamics and rigorously demonstrate the existence of chaos. Furthermore, we formulated an optimal control problem that describes the dynamics of tumour-immune interactions, considering treatments such as radiotherapy and chemotherapy as control parameters. Our goal is to utilize optimal control theory to reduce the cost of radiotherapy and chemotherapy, minimize the harmful effects of medications on the body, and mitigate the burden of cancer cells by maintaining a sufficient population of healthy cells. Cost-effectiveness analysis is employed to identify the most economical strategy for reducing the disease burden. Additionally, we conduct a Latin hypercube sampling-based uncertainty analysis to observe the impact of parameter uncertainties on tumour growth, followed by a sensitivity analysis. Numerical simulations are presented to elucidate how dynamic behaviour of model is influenced by changes in system parameters. The numerical results validate the analytical findings and illustrate that a multi-therapeutic treatment plan can effectively reduce tumour burden within a given time frame of therapeutic intervention.

We consider a three-dimensional mathematical model that describes the interaction between the effector cells, tumor cells, and the cytokine (IL-2) of a patient. This is called the Kirschner–Panetta model. Our objective is to explain the tumor oscillations in tumor sizes as well as long-term tumor relapse. We then explore the effects of adoptive cellular immunotherapy on the model and describe under what circumstances the tumor can be eliminated or can remain over time but in a controlled manner. Nonlinear dynamics of immunogenic tumors are given, for example: we prove that the trajectories of the associated system are bounded and defined for all positive time; there are some invariant subsets; there are open subsets of parameters, such that the system in the first octant has at most five equilibrium solutions, one of them is tumor-free and the others are of co-existence. We are able to prove the existence of transcritical and pitchfork bifurcations from the tumor-free equilibrium point. Fixing an equilibrium and introducing a small perturbation, we are able to show the existence of a Hopf periodic orbit, showing a cyclic behavior among the population, with a strong dominance of the parental anomalous growth cell population. The previous information reveals the effects of the parameters. In our study, we observe that our mathematical model exhibits a very rich dynamic behavior and the parameter $\tilde{\mu }$ (death rate of the effector cells) and ${\tilde{p}}_1$ (production rate of the effector cell stimulated by the cytokine IL-2) plays an important role. More precisely, in our approach the inequality ${\tilde{\mu }}_2>{\tilde{p}}_1$ is very important, that is, the death rate of the effector cells is greater than the production rate of the effector cell stimulated by the cytokine IL-2. Finally, medical implications and a set of numerical simulations supporting the mathematical results are also presented.

SARS-CoV-2 has the ability to form large multi-nucleated cells known as syncytia. Little is known about how syncytia affect the dynamics of the infection or severity of the disease. In this manuscript, we extend a mathematical model of cell–cell fusion assays to estimate both the syncytia formation rate and the average duration of the fusion phase for five strains of SARS-CoV-2. We find that the original Wuhan strain has the slowest rate of syncytia formation ($6.4\times 10^{-4}/h$), but takes only 4.0 h to complete the fusion process, while the Alpha strain has the fastest rate of syncytia formation (0.36 /h), but takes 7.6 h to complete the fusion process. The Beta strain also has a fairly fast syncytia formation rate ($9.7\times 10^{-2}/h$), and takes the longest to complete fusion (8.4 h). The D614G strain has a fairly slow syncytia formation rate ($2.8\times 10^{-3}/h$), but completes fusion in 4.0 h. Finally, the Delta strain is in the middle with a syncytia formation rate of $3.2\times 10^{-2}/h$ and a fusing time of 6.1 h. We note that for these SARS-CoV-2 strains, there appears to be a tradeoff between the ease of forming syncytia and the speed at which they complete the fusion process.

This article addresses reaction networks in which spatial and stochastic effects are of crucial importance. For such systems, particle-based models allow us to describe all microscopic details with high accuracy. However, they suffer from computational inefficiency if particle numbers and density get too large. Alternative coarse-grained-resolution models reduce computational effort tremendously, e.g., by replacing the particle distribution by a continuous concentration field governed by reaction–diffusion PDEs. We demonstrate how models on the different resolution levels can be combined into hybrid models that seamlessly combine the best of both worlds, describing molecular species with large copy numbers by macroscopic equations with spatial resolution while keeping the spatial–stochastic particle-based resolution level for the species with low copy numbers. To this end, we introduce a simple particle-based model for the binding dynamics of ions and vesicles at the heart of the neurotransmission process. Within this framework, we derive a novel hybrid model and present results from numerical experiments which demonstrate that the hybrid model allows for an accurate approximation of the full particle-based model in realistic scenarios.

This paper addresses the problem of designing a safe and optimal control strategy for typical cancer using the Control Barrier Function (CBF) technique. Cancer is a complex and highly dynamic disease characterized by uncontrolled cell growth and proliferation. By formulating the cancer dynamics as a control system, this study introduces a CBF-based controller that guides the cancerous tissue towards safe and controlled behaviors. The controller is designed to simultaneously optimize treatment efficacy and patient safety. The methodology involves modeling the cancer growth dynamics, incorporating relevant biological constraints, and designing the CBF-based controller to regulate the tumor’s evolution within acceptable bounds. Simulation results demonstrate the effectiveness of the CBF-based strategy in achieving safe and optimal cancer control. The controller showcases the ability to drive the cancerous tissue towards desired states while respecting predefined safety constraints.

Based on a deterministic and stochastic process hybrid model, we use white noises to account for patient variabilities in treatment outcomes, use a hyperparameter to represent patient heterogeneity in a cohort, and construct a stochastic model in terms of Ito stochastic differential equations for testing the efficacy of three different treatment protocols in CAR T cell therapy. The stochastic model has three ergodic invariant measures which correspond to three unstable equilibrium solutions of the deterministic system, while the ergodic invariant measures are attractors under some conditions for tumor growth. As the stable dynamics of the stochastic system reflects long-term outcomes of the therapy, the transient dynamics provide chances of cure in short-term. Two stopping times, the time to cure and time to progress, allow us to conduct numerical simulations with three different protocols of CAR T cell treatment through the transient dynamics of the stochastic model. The probability distributions of the time to cure and time to progress present outcome details of different protocols, which are significant for current clinical study of CAR T cell therapy.

A dynamic model is proposed to describe a mycoloop in aquatic food webs. The model consists of phytoplankton, chytrids and zooplankton. It characterizes that zooplankton consume both phytoplankton and free-living chytrid spores, and that chytrids infect phytoplankton. The dynamics of the model are investigated containing the dissipativity, existence and stability of equilibria, and persistence. The ecological reproductive indexes for phytoplankton or zooplankton invasion and basic reproduction numbers for chytrid transmission are derived. The parameter values of the model are estimated based on experimental data. Numerical simulations explore the effects of the mycoloop on phytoplankton blooms and chytrid transmission. This research reveals that the mycoloop structure increases or reduces phytoplankton blooms, and controls the spread of chytrids among phytoplankton.

The unprecedented scale and rapidity of dissemination of re-emerging and emerging infectious diseases impose new challenges for regulators and health authorities. To curb the dispersal of such diseases, proper management of healthcare facilities and vaccines are core drivers. In the present work, we assess the unified impact of healthcare facilities and vaccination on the control of an infectious disease by formulating a mathematical model. To formulate the model for any region, we consider four classes of human population; namely, susceptible, infected, hospitalized, and vaccinated. It is assumed that the increment in number of beds in hospitals is continuously made in proportion to the number of infected individuals. To ensure the occurrence of transcritical, saddle–node and Hopf bifurcations, the conditions are derived. The normal form is obtained to show the existence of Bogdanov–Takens bifurcation. To validate the analytically obtained results, we have conducted some numerical simulations. These results will be useful to public health authorities for planning appropriate health care resources and vaccination programs to diminish prevalence of infectious diseases.