This study proposes a nonlinear mathematical model of virus transmission based on the SEIR model. In this study, the interaction between viruses and immune cells is investigated using phase-space analysis of a mathematical model. Specifically, it is focused on the dynamics and stability behavior of the mathematical model of a virus spread in a population and its interaction with human immune systems cells. The endemic equilibrium points are found and local stability analysis of all equilibria points of the related model is obtained. Further, the global stability analysis either, at disease-free equilibria, or in endemic equilibria is discussed by constructing the Lyapunov function which shows the validity of the concern model exists. Finally, a simulated solution is achieved and the relationship between viruses and immune cells is highlighted.

This paper presents a comprehensive investigation into the applicability and performance of two prominent growth models, namely the Verhulst model and the Montroll model, in the context of modeling tumor cell growth dynamics. Leveraging the power of Physics-Informed Neural Networks (PINNs), we aim to assess and compare the predictive capabilities of these models against experimental data obtained from the growth patterns of tumor cells. We employ a dataset comprising detailed measurements of tumor cell growth to train and evaluate the Verhulst and Montroll models. By integrating PINNs, we not only account for experimental noise but also embed physical insights into the learning process, enabling the models to capture the underlying mechanisms governing tumor cell growth. Our findings reveal the strengths and limitations of each growth model in accurately representing tumor cell proliferation dynamics. Furthermore, the study sheds light on the impact of incorporating physics-informed constraints on the model predictions. The insights gained from this comparative analysis contribute to advancing our understanding of growth models and their applications in predicting complex biological phenomena, particularly in the realm of tumor cell proliferation.

The proliferation of SARS-COV-2 through enhanced viral replication and its subsequent triggering of cytokine storm, are some of the hallmark phenotypes in severe COVID-19 patient cases. Cyclosporine, an immunosuppressant drug and Selinexor, an inhibitor of nuclear transporter protein, both have been successfully demonstrated to be effective against SARS-COV-2 infection by targeting those functions individually. However, the highly multifactorial pathology of SARS-COV-2 infection hinders any mono-therapeutic strategy to become an optimal option. In this study, we assess the potential efficacy of the Cyclosporine-Selinexor combination on an integrated interactome by adopting a network-medicine-based repositioning technique, where disease proximity, functional proximity and their topological separation are evaluated, followed by a robust statistical significance test. Results have shown that both drug target modules are highly proximal to the SARS-COV-2 disease modules in terms of network topology and functional associations, in a statistically significant manner, individually. Functional enrichment of both drug modules and SARS-COV-2 infected modules has shown that two drugs target the functions related to viral replication and cytokine storm during infection. Moreover, a high degree of network separation been those two drug target modules has been observed, revealing ``complementary exposure`` patterns, rendering this drug combination as an effective one against SARS-COV-2 infection. We hope that our results will encourage researchers to further investigate the potency of Cyclosporine and Selinexor combination in vivo or in vitro, and ultimately lead that up to clinical trials to treat SARS-COV-2 patients.

Drug-target affinity (DTA) prediction is crucial for understanding molecular interactions and aiding drug discovery and development. While various computational methods have been proposed for DTA prediction, their predictive accuracy remains limited, failing to delve into the structural nuances of interactions. With increasingly accurate and accessible structure prediction of targets, we developed a novel deep learning model, named S2DTA, to accurately predict DTA by fusing sequence and structural knowledge of drugs, targets, and pockets using heterogeneous models based on graph and semantic networks. Experimental findings underscored that complex feature representations imparted negligible enhancements to the model’s performance. However, the integration of heterogeneous models demonstrably bolstered predictive accuracy. In comparison to three state-of-the-art methodologies, the supremacy of S2DTA became strikingly apparent. It showcased a noteworthy 25.2% reduction in Mean Absolute Error (MAE) and an impressive 20.1% decrease in Root Mean Square Error (RMSE). Furthermore, S2DTA exhibited substantial advancements in other pivotal metrics, including Pearson Correlation Coefficient (PCC), Spearman, Concordance Index (CI), and R2. These metrics experienced remarkable increments of at least 19.6%, 17.5%, 8.1%, and a remarkable 49.4%, respectively. Finally, we conducted interpretability analysis on the effectiveness of S2DTA by bidirectional self-attention mechanism, fully proving that S2DTA is a valuable and accurate tool for predicting DTA. For further exploration, the source data and code repository can be accessed at https://github.com/dldxzx/S2DTA.

Visual exploration of complex data helps interpretation, especially in the case of omics data analysis in life sciences and clinical research. Generating and analysing omics data requires bioinformatic skills, while they are interpreted by domain experts, for whom parsing large and complex data structures may be challenging. However, outcomes of visual analytics are often difficult to quantify, which emphasises precision and reproducibility, especially for research on human diseases. Here, we propose a workflow combining a reproducible computational environment with a dedicated visualisation functionality for systems biology diagrams. By linking the Galaxy with the MINERVA Platform, we visualise and explore COVID-19 transcriptomic data to demonstrate the utility of our workflow. Visualised data recapitulate findings of the original publication and offer new insights about the COVID-19 pathology. Our results offer a blueprint for quick prototyping of computational workflows that facilitate communication and exploration of complex data in biomedical research.

We here investigate the dynamical behavior of a fractional-order predator-prey system with anti-predator behavior and Holling IV type functional response. First we study the non-negativity, existence, uniqueness, and boundedness of solutions to the system from a mathematical analysis perspective. Then, we analyze the stability of its equilibrium points and the possibility of bifurcations using stability analysis methods and bifurcation theory, and prove the existence of a supercritical Hopf bifurcation in the system. After providing numerical simulations to illustrate the conclusions theoretically derived, by summarizing those various analytical results obtained, we finally present three interesting conclusions that can contribute to better understanding and preservation of ecological systems.

Antiangiogenic therapy (AAT) is an indirect oncological modality which is aimed at disruption of cancer cells nutrient supply. Invasive tumors have been shown to possess inherent resistant to this treatment, while compactly growing benign tumors react to it by shrinkage. It is generally accepted that AAT by itself is not curative. This study presents a mathematical model of non-invasive tumor growth with physiologically justified account of alteration of microvasculature and biomechanical aspects during tumor growth and AAT. In untreated setting the model reproduces tumor growth with saturation, where the maximum tumor volume depends on the level of angiogenesis. The outcomes of simulations of AAT depend on the tumor size at the moment of treatment initiation. If it is close to the stable size of avascular tumor grown in absence of angiogenesis, then the tumor is rapidly stabilized by AAT. Treatment of large tumors is accompanied by displacement of normal tissue due to the tumor shrinkage. During it, microvasculature undergoes distortion which degree depends on the displacement distance. As it affects tumor nutrient supply, the stable size of a tumor that undergoes AAT negatively correlates with its size at the beginning of treatment. For sufficiently large initial tumors, the long-term survival of tumor cells is compromised by competition with normal cells for severely limited inflow of nutrients, which makes AAT effectively curative.

This paper proposes an imperfectly vaccinated SVEIR model for latent age. We calculate the equilibrium points and basic reproduction number of the model. The asymptotic smoothness, uniform persistence and the existence of the attractor of the semi-flow generated by the solutions of the system are addressed. Moreover, using LaSalle’s invariance set principle and constructing Volterra-type Lyapunov functions, we can prove the global asymptotic stability of both the disease-free equilibrium and the endemic equilibrium of the model. The conclusion is that if the basic reproduction number R0 is less than one, the disease will gradually disappear. On the other hand, if the number is greater than one, the disease will become endemic and persist. Finally, measures that can effectively control the ongoing transmission of the disease have been obtained.

This article focuses on the analysis of dynamics emerging in a Network of Hodgkin-Huxley Reaction-Diffusion equations. The network is forced with three external periodic stimulus input. A synchronization phenomenon is observed.

We investigate a new fundamental property of infectious diseases with natural adaptive immunity that weakens over time. Numerical experiments with a model of the Covid-19 epidemic in Moscow have demonstrated that when the reproduction number R0 is about 4, a qualitative change (bifurcation) occurs in the behavior of the virus-human system. Below this value, the long-term forecast tends to undamped oscillations; above it, the forecast shows damped oscillations: the amplitudes of epidemic waves decrease gradually, with a constant, very high background level of morbidity that keeps the natural immunity near 100%. To confirm this result analytically, we use an original modification of the Euler-Lotka renewal equation, which describes the dynamics of infected patients distributed by disease duration (time since infection) and accounts for immunity. To construct a bifurcation diagram, which illustrates the dependence of the equilibrium stability on the parameter R0, we linearize the equation in the vicinity of the equilibrium point and examine its numerical approximation (discrete form). This approximation can be interpreted as a Leslie model, with the matrix elements dependent on the parameter R0. By examining the roots of the corresponding Lotka polynomial, we can assess the stability of the equilibrium point. For the bifurcation diagram, we use the functions obtained from the simulation of the Covid-19 epidemic in Moscow. However, observations of the epidemic in other cities and countries support the primary finding of our study regarding the attenuation of epidemic waves.

The paradigm of molecular communications is applied to the concrete case for delivering electrically charged nanoparticles to tumor. Once them have been injecetd in blood it is expecetd an optimal outcome as to reduce toxicity and minimal dispersion of drugs in the blood stream. With a fraction of nanoparticles arrives to surface of tumor, the scattered part of injected ones can minimize the success of scheme of drug delivery. In this paper is presented a theory based at the sequence electrodynamics-diffusion-Bayes theorem. The resulting probability of Bayes at the end of sequence, might be telling us that dynamical processes based in the injection of electrically charged nanoparticles might be dictated by stochastic formalism more that biochemical approaches by which makes impossible to know the success or fail of drug delivery dynamics. Illustrations demonstrating the transition of a linear to nonlinear scenario are presented

This study investigates the stochastic dynamics of hepatitis B virus (HBV) infection using a newly proposed stochastic model. Contrary to deterministic models that fail to encapsulate the inherent randomness and fluctuations in biological processes, our stochastic model provides a more realistic representation of HBV infection dynamics. It incorporates random variability, thereby acknowledging the changes in viral and cellular populations and uncertainties in parameters such as infection rates and immune responses. We examine the solution's existence, uniqueness, and positivity for the proposed model, followed by a comprehensive stability analysis. We provide the necessary and sufficient conditions for local and global stability, offering deep insight into the infection dynamics. Furthermore, we utilize numerical simulations to corroborate our theoretical results. This research provides a robust tool for understanding the complex behavior of HBV dynamics, contributing significantly to the ongoing quest for more effective HBV control and prevention strategies.

Bipolar disorder is a severe mood disorder and is one of the top 20 reasons of disability in the world. It causes a huge burden on society. In this study, the prediction models of bipolar disorder were constructed based on the concept of knowledge distillation. The input data consisted of patients of bipolar disorder and matched controls, all of which were selected from the open database MIMIC. The method of kernel density estimation (KDE) was exploited to generate probability density functions (PDF) which identify distributions of input data. The PDF values referred to as the soft labels were combined with the input data to construct the prediction models of bipolar disorder using decision tree and artificial neural network respectively. According to the evaluation results, indicators for identifying positive samples of bipolar disorder were improved. Meanwhile, the indicators for identifying negative samples have also been advanced. In addition, the branching attributes selected by the decision trees can be mapped back to specific disease diagnoses, which are all associated with bipolar disorder. In conclusion, using KDE to generate the soft label information of the input data can make knowledge distillation work and has improved the performances of prediction models for bipolar disorder.

A closed chain of oscillators can be considered as a model of ring-shaped ecosystems, such as atolls or coastal zones of inland reservoirs. As an oscillator model, we use the logistic map that often referred to as an archetypical example of how complex dynamics can arise from very simple nonlinear equations. We investigate the influence of the model parameters both on the nature of oscillations in the oscillator ring and on the spatial structures that arise in this case. Namely, we demonstrate a variety of emerging spatial structures depending on the initial conditions.

We give a series of numerical examples of competitive evolution in the predation system, showing in some cases how the choice is made to increase the efficiency of the predation mechanism (or other significant parameters) to the detriment of populations (both of prey and predators). We then develop the mathematical theory that enables us to understand the causality involved, and identify a trend towards the emergence of the functional predation mechanism as such (and not of populations of the species involved). The realization of this trend only takes place when the conditions for it are offered by the hazards proposed to successive competitive choices. The logical structure of this trend is similar to that of the « tendency of rate of profit to fall » in certain economic models.