We investigate the impact of the weak Allee effect on the total biomass of a single species inhabiting a two-patch environment connected by asymmetric dispersal. In the proposed model, the first patch exhibits logistic growth, while the second patch follows a weak Allee threshold. We establish the global existence, nonnegativity, and boundedness of solutions, and prove that the system admits a unique positive equilibrium that is globally asymptotically stable. Analytical results are derived for the asymptotic regime of high dispersal rates using singular perturbation theory, revealing an emergent weak Allee effect at the metapopulation scale. We conduct a complete classification of the parameter space to determine when dispersal increases, decreases, or has a unimodal effect on total equilibrium biomass, and provide geometric and monotonicity analyses of the equilibrium. Numerical simulations illustrate the theoretical trichotomy and highlight the ecological implications of dispersal management in fragmented landscapes. Our results generalize previous studies on logistic models to include the weak Allee effect, offering new insights into the interplay between dispersal intensity, asymmetry, and population persistence.
HIV/AIDS remains a major public health challenge in South Africa, where denialism continues to undermine prevention and treatment efforts. This study develops a mathematical transmission model that explicitly incorporates denial behaviours, including refusal of preventive measures, refusal to initiate antiretroviral therapy (ART), and discontinuation of ART. Analytical and simulation results show that denial substantially increases HIV incidence, accelerates progression to AIDS, and raises the likelihood of a backward bifurcation, an occurrence where HIV may persist even when the basic reproduction number falls below one. Sensitivity analysis identified denial-related transmission as a key driver of epidemic dynamics. These findings underscore the need to address denialism by strengthening HIV testing, ART uptake and retention, and community-level education to counter misinformation and stigma.
We consider the nonparametric maximum likelihood estimation of single type discrete time branching processes with random migration. These processes occur naturally in situations where besides the random reproduction both emigration and immigration of individuals can be observed in the population. Our aim is to study the behaviour of the estimators by calculating the Fisher information matrix and in particular to present confidence intervals for the migration probabilities and for the offspring and immigration distribution, which to be further examined by simulations and computational results.
The fall armyworm Spodoptera frugiperda, hereafter referred to as FAW, is one of the most destructive invasive pests affecting maize production in sub-Saharan Africa. Understanding how climatic variability influences its population dynamics is essential for improving pest monitoring and management strategies. In this study, we develop and analyze a stage-structured mathematical model describing the population dynamics of the pest across its four developmental stages (eggs, larvae, pupae, and adults). We first investigate a baseline model with constant parameters, which allows a complete mathematical analysis of the system. A threshold quantity governing pest extinction or persistence is derived, and sensitivity analysis identifies the biological parameters that most strongly influence population growth. These results provide theoretical insights into which life stages represent the most effective targets for control strategies. We then extend the framework to incorporate climate-driven dynamics through temperature- and rainfall-dependent parameters. Using climatic observations from Pretoria (South Africa), we examine how seasonal environmental variability affects pest persistence. The analysis leads to the identification of two climate-dependent thresholds, R0min and R0max, which determine whether the pest population disappears or persists through periodic seasonal oscillations. Numerical simulations illustrate how climatic forcing can generate contrasting invasion scenarios and reproduce realistic seasonal patterns of pest abundance. Overall, the proposed framework highlights the central role of climatic variability in shaping FAW population dynamics and demonstrates how climate-informed mathematical models can serve as predictive tools for agricultural pest monitoring and integrated pest management.
The dynamics of blood flow are dramatically changed by arterial stenosis, a leading cause of cardiovascular diseases. The hemodynamics through a bell-shaped stenosis are examined in this work, which increases with time. A new model is developed after incorporating the temporal term in the geometry of the bell-shaped stenosis. The equation is then solved to get analytical solutions of the flow parameters for axisymmetric, incompressible, and fully developed flow, taking blood as a non-Newtonian fluid. Important variables, including viscosity, time, and stenosis geometry, are changed to see how they affect the volumetric flow rate, velocity, pressure drop, pressure drop ratio, shear stress, and shear stress ratio. The findings demonstrate a large drop in velocity and volumetric flow rate at the bell-shaped stenotic region with increasing time and viscosity. In the region of bell-shaped stenosis, pressure drop and wall shear stress and their ratios increase rapidly with increasing stenosis. These results demonstrate how important the bell-shaped progressive stenosis is to prevent blood flow and raise the risk of cardiovascular disease. It can be used for the clinical approach and for the researchers in this field.
This study develops an integrated mathematical model of the cardiovascular–respiratory system to investigate the regulation of blood and gas pressure dynamics during physical exercise in a Chadian athletic population. Heart rate and alveolar ventilation are incorporated as control inputs within an optimal control framework to explain the stabilization of systemic arterial pressure (Pas), systemic venous pressure (Pvs), and arterial partial pressures of oxygen (PaO2) and carbon dioxide (PaCO2) during moderate and intense exercise. The model is calibrated using field data collected from elite male and female football players and discretized using B-spline basis functions to compute optimal control trajectories. Simulation results show a strong concordance between the measured physiological variables and the model predictions, as confirmed by the RMSE and MAE values reported in Tables 7 and 8. Moreover, clear sex-related ventilatory differences emerge from the simulations: under comparable exercise intensity, male and female athletes exhibit a measurable gap in alveolar ventilation, with a difference quantified as Δ VA = 1.8 L·min-1. The objective of this modeling approach is primarily explanatory rather than predictive, aiming to reproduce and interpret the physiological mechanisms governing cardiorespiratory adaptation to exercise rather than to provide long-term individual predictions. The proposed framework demonstrates the capacity of optimal control–based models to capture realistic, population-specific cardiorespiratory responses and provides a foundation for future refinement and validation using larger experimental datasets.
Discrete-time epidemic models may display rich dynamics, including oscillatory outbreaks and chaotic behavior arising through period-doubling (Flip) bifurcations when key parameters, such as transmission or recruitment rates, vary. In most optimal control studies, the main objective is to reduce infection prevalence and intervention cost, while the possible impact of bifurcation-induced qualitative changes is often left aside. In this paper, we propose a bifurcation-aware optimal control framework for a discrete-time SIRS epidemic model that aims not only to reduce infection levels and control effort, but also to suppress multi-wave epidemic behavior. We first study the equilibria of the controlled system and derive the corresponding controlled basic reproduction number. We then analyze the local stability of the endemic equilibrium through the Jacobian spectrum and introduce a practical Flip-proximity indicator, based on the distance of eigenvalues to -1, in order to identify regimes that are close to period-doubling. Motivated by this analysis, we formulate a discrete-time optimal control problem with two intervention mechanisms: modulation of population recruitment and reduction of disease transmission. To discourage persistent oscillatory behavior in the infected population, we include an additional oscillation-penalty term in the objective functional, which serves as a control-oriented surrogate for limiting higher-period outbreak patterns. The resulting optimality system is derived by means of a discrete Pontryagin maximum principle and solved numerically using a projected forward-backward algorithm under bounded control constraints. Numerical results indicate that the proposed strategy leads to smoother infection profiles, lower peak prevalence, and a greater tendency to avoid flip-prone regimes than standard quadratic-cost control formulations.
The control of chemotactic systems is a critical challenge in applied mathematics, with direct implications for biomedical applications such as cancer therapy. In this paper, we investigate a degenerate Keller--Segel model with a spatiotemporal control input, representing the addition or elimination of chemical concentration. The model is discretized using a finite element scheme, and an adjoint-based optimization algorithm is employed to design effective control strategies. Numerical simulations confirm the stability and efficiency of the method: the cost functional and gradient norm decrease rapidly, the error stabilizes at small values, and both cell density and chemoattractant concentration are successfully reduced. These results demonstrate how numerical analysis provides reliable insights into regulating chemotaxis and highlight its potential for guiding therapeutic dosing strategies.
Mathematical modeling can perform a decisive task in understanding, controlling, and preventing the transmission of infectious diseases by forecasting their spread, estimating the effectiveness of intervention measures, and updating public health policies. A mathematical epidemic model is a vital tool that can mock up the spread of infections under different scenarios and environments, allowing researchers to test and refine their understanding of the fundamental mechanisms. This paper attempts to review some existing mathematical compartmental epidemic models and explore the impact of meteorological factors such as air temperature, humidity, and wind speed on epidemiology. The goal is to identify and categorize key components, research trends, major findings, and gaps within the models. Additionally, the paper discusses some strategies to address these gaps and proposes a compartmental augmentation of the SEIR model incorporating meteorological factors for further work.
Type 1 diabetes mellitus (T1DM) is a chronic autoimmune condition marked by the pancreas's failure to generate insulin, requiring exogenous insulin for glucose regulation. This study investigates the combined impact of stress, diet, and physical exercise on blood glucose levels and overall health outcomes in individuals with T1DM who are on exogenous insulin therapy and live different lifestyles by formulating a mathematical model to capture the dynamic interactions between insulin requirements and blood glucose regulation analytically and numerically. The model's boundedness, equilibrium stability, and the characteristics of equilibrium values for glucose and insulin concentrations are addressed as well as our proposed model demonstrates asymptotic stability at the equilibrium point. The result of numerical simulation highlights that even after taking three doses of insulin daily, a patient's glucose levels might rise if they do not exercise regularly and are under a lot of stress. Furthermore, findings from this research suggest that a healthy diet plan serves as an essential part for individuals with type 1 diabetes to regulate their blood sugar levels through ensuring that insulin is activated correctly.
S-shaped curves are ubiquitous in biology especially when it comes to growth of a population or even an individual. Growth models such as the classical Verhulst-Pearl logistic growth equation and its extensions effectively model such S-shaped growth curves. Most of these models are parametrized by three or more parameters. In this work, continued fraction of straight lines has been applied to model S-shaped curves of biological growth through the use of only two parameters a and m. Here, m is the maximum growth rate and a is the parameter restricting the growth rate. The parameters a and m help to better interpret the data when compared to the logistic growth model since m represents factors promoting growth while a represents restricting factors of growth. This model is effective for modeling both population as well as individual growth, especially around the phase of rapid growth.
This study applies a graph-theoretic framework to analyze the structural dynamics of codon networks derived from SARS-CoV-2 spike protein sequences. By employing a dual-level analysis of Minimum Connected Dominating Sets (MCDS) and community structures, we explore the mathematical underpinnings of viral protein organization. First, we construct the MCDS to identify critical codons that ensure global network connectivity, providing key insights into structurally significant regions of the protein sequence. Next, we analyze the community structures within the network to determine localized structural and functional roles, facilitating the identification of specialized codon groups. Centrality measures are employed to quantify the significance of codons within both the MCDS and the identified communities, highlighting their roles in maintaining network integrity. Furthermore, we investigate the impact of mutations across SARS-CoV-2 variants, assessing their influence on codon connectivity and functional stability. A statistical analysis of MCDS and community node variability provides deeper insights into the structural robustness of the spike protein. This study underscores the potential of mathematical modeling in virology and highlights essential codons as potential targets for therapeutic intervention.
This work constructs a generic model for chemo-immunotherapy of cancer in a healthy tissue. The main interests are the modeling and computer study of chemotherapy, immunotherapy and the advantages in their combined applications. It describes the dynamics of Healthy, Immune, and Cancer cells when chemotherapy and immunotherapy are applied, either separately or combined. The analysis of the model shows that its solutions exist, are bounded and nonnegative on each finite time interval, and thus are biologically feasible. The model simulations describe the development of the disease without intervention, when only chemotherapy or immunotherapy are administered periodically, when the two modalities are combined. In this manner, once validated, the model can be used to design treatment schedules for improved outcomes.
In this work, we investigate the existence of multistationarity for a triple-site mixed phosphorylation network, where the phosphorylation part contains distributive and processive components, while the dephosphorylation part is purely distributive. We obtain a simple inequality which defines a region in parameter space such that the parametric ordinary differential equations (ODE) system modeling the mixed network is multistationary, i.e., it has multiple positive steady states. We obtain a sufficient condition for uniqueness of the steady state in the form of parametric inequalities. Lastly, we show that the emergence of multistationarity is enabled by the catalytic constants regardless of the position of the processive part in the triple-site mixed mechanism phosphorylation network.
The formation of stenosis in the lumen obstructs the normal flow and causes disorders in the cardiovascular system, which becomes riskier due to the curvature of the artery. The curvature affects the blood flow system directly by reducing the velocity, which helps increase the thickness of the stenosis. In this article, the effect of curvature on the stenosed part of an artery is studied using the Navier-Stokes equation in cylindrical polar form. A new model is developed by incorporating a term in quadratic form to address the joint effect of stenosis and curvature upon flow parameters. This model equation with appropriate boundary conditions is solved to get analytical solutions for velocity, volumetric flow rate, pressure drop ratio, and shear stress ratio, and all the results are analyzed geometrically. The results show that when the curvature increases, the pressure drop ratio and shear stress ratio increase, while the velocity and volumetric flow rate decrease. Quantitative effect of the curvature on flow parameters is visualized which may help researchers in the related field.
I present a new dose-survival equation for fitting clonogenic assay data collected for irradiated cells, one motivated by the hypothesis that all cellular activities can be partitioned into two states (“state R” and “state Q”) which differ in their sensitivity to low-LET radiation. The LQ model can be derived from it by taking a Taylor expansion. The empirical observation that rapidly proliferating cancer cells have a straighter dose-survival relationship, while slowly proliferating cancer cells and normal cells have a curvier one featuring a shoulder region, is explained in terms of state R and state Q. The new equation (1) provides a convention for classifying cells as radioresistant, (2) provides a means of reducing, or possibly eliminating, cell cycle phase as a variable in treatment outcome, and (3) may enable standardization of the results reported for clonogenic assays. Finally, a novel hypothesis is offered for the “oxygen enhancement ratio” phenomenon.
By considering the recently introduced SIRU model, in this paper we study the dynamic of COVID-19 pandemic under the temporally varying public intervention in the Chilean context. More precisely, we propose a method to forecast cumulative daily reported cases CR(t), and a systematic way to identify the unreported daily cases given CR(t) data. We firstly base on the recently introduced epidemic model SIRU (Susceptible, Asymptomatic Infected, Reported infected, Unreported infected), and focus on the transmission rate parameter τ. To understand the dynamic of the data, we extend the scalar τ to an unknown function τ(t) in the SIRU system, which is then inferred directly from the historical CR(t) data, based on nonparametric estimation. The estimation of τ(t) leads to the estimation of other unobserved functions in the system, including the daily unreported cases. Furthermore, the estimation of τ(t) allows us to build links between the pandemic evolution and the public intervention, which is modeled by logistic regression. We then employ polynomial approximation to construct a predicted curve which evolves with the latest trend of CR(t). In addition, we regularize the evolution of the forecast in such a way that it corresponds to the future intervention plan based on the previously obtained link knowledge. We test the proposed predictor on different time windows. The promising results show the effectiveness of the proposed methods.
We develop a within-host mathematical model for hepatitis B virus infection that leads to hepatocellular carcinoma incorporating immunotherapy as an intervention strategy and also demonstrating drug effects in the sub-therapeutic, therapeutic and toxicity regions of concentration. The model includes the dynamics of hepatocytes, immune cells, cytokines and hepatitis B virus dynamics using a system of ordinary differential equations. Model parameters were estimated using the flexible modeling environment algorithm. Treatment was presented replicating realistic pharmacokinetics of a drug called Nivolumab as a monoclonal antibody type of immunotherapy. Results suggests that immunotherapy reduces the growth of cancer cells when the drug concentration is in a therapeutic region but complete eradication is not possible. Drug concentration above the therapeutic region reduced the cancer cells to better levels but this benefit is associated with toxicity of the drug. Drug concentration below the therapeutic region is associated with little reduction in cancer cells.
We consider the acetogenesis and hydrogenotrophic methanogenesis phases of the anaerobic digestion model and we include the inhibition of methanogenics, first by volatile fatty acids (VFAs) then by acetogenics. We investigate mathematically the dynamics of two chemostat models described by systems of four nonlinear ordinary differential equations. We established the conditions of existence and stability of equilibrium points in each of the models with respect to the dilution rate. The operating diagrams allowed to reveal the similarities and the differences between regions of stability of the two models and to present the consequent transcritical bifurcations between boundary and positive equilibrium. Models are equivalent for low inlet substrate concentration and significantly different for high concentration. When inhibition is by acetogens and for high concentrations of inlet substrate, the upstream species tends to eliminate the downstream species from the vessel.
This work constructs, analyzes and simulates the SIR-IH model, a modified SIR epidemiological model for the spread of a disease, in which the infection rate and hospitalization ratio are system variables. The motivation, in part, of making the infection rate a state variable comes from the observations that the infectivity of a disease, such as COVID-19, has been changing with the evolution of the disease, and not necessarily by the appearance of new variants. Moreover, it may change in time if more than one variant are present. The addition of a hospitalization rate is done to make the model more applied for those who need to make decisions on the preparedness of the health system, in particular the hospitals, in case of a pandemic. The model consists of a coupled system of differential equations, and its analysis shows the existence, positivity and boundedness of the solutions. Then, computer simulations depict some typical or interesting dynamic behaviors, and the way the system approaches the steady states.
