Dengue remains a public health challenge due to the persistence of Aedes aegypti populations and the limited effectiveness of medical and vector control interventions. The release of Wolbachia-infected mosquitoes has been used in multiple regions; yet, release protocols are often heuristically structured, with limited optimization. In particular, the impacts of mosquito sex structure and strain-specific effects remain unclear. This study develops a sex-structured dynamical model that links within-vector Wolbachia dynamics, such as cytoplasmic incompatibility and vertical transmission, with between-host dengue transmission. An optimal control framework is used to determine cost-effective releases of male and female mosquitoes over a finite intervention horizon, with mosquito dispersal on a finite time interval. The cost effectiveness of a release program relies on minimizing releases and dengue cases. The approach is applied to three Wolbachia strains, wAlbB, wMel, and wMelPop, to assess how strain-specific fitness and viral blocking influence optimal release plans. The analysis identified sex-structured strategies that diverge from in-field protocols, supporting the notion that commonly used plans may benefit from optimization by sex. Additionally, differences were noted among strains, which suggests that optimal sex-structured releases may vary with Wolbachia strain used.
We develop a unified uncertainty propagation framework for computational models involving stochastic variability together with two distinct forms of epistemic uncertainty: vagueness and incomplete knowledge. In this framework, stochastic uncertainty is represented by random variables, while the epistemic components are modeled by random fuzzy sets with fuzzy mass functions generalized from Dempster-Shafer theory and fuzzy set theory. Using generalized polynomial chaos expansions and extension principles, the propagated uncertainty in output expectation is then quantified efficiently by a fuzzy mass function. We also introduce a distance measure between fuzzy mass functions and use it to analyze the error in the resulting numerical approximations. The proposed approach is demonstrated on several simple examples and applied to two biological systems: the Mitchell-Schaeffer model governed by a system of ordinary differential equations, and a computational model of olfaction governed by the Navier-Stokes equations.
The phenomenon of inflammation is increasingly being implicated as a promoter of cancer development. Accordingly, linkages between different cancer types and inflammation are traced. Findings in the biomedical literature related to inflammatory footprints in cancer development are highlighted. Existing mathematical models, even though few, that involve inflammation and cancer are reviewed. With emphasis on the need for increased modeling activity in the area, the biomedical discussions and modeling reviews then lead into the proposal of a simple mathematical model that serves as an additional candidate model for studying cancer dynamics in an inflammatory environment. This is looked at as a way of building upon the relatively few mathematical modeling approaches that may be useful for providing insights as the biomedical studies and investigations proceed. The proposed model consists of a system of three ordinary differential equations tracking the interaction dynamics of cancer cells, inflammatory cells, and normal tissue. Subsequently, model steady states are analyzed and most importantly given necessary interpretations in biomedical contexts. To address parameter variability, uncertainty analysis using Latin Hypercube sampling is used to explore output uncertainty, while partial rank correlation coefficient (PRCC) sensitivity analysis identifies key driving parameters. PRCC analysis identifies three immunologically distinct pathways: one drives a protective anti-tumor response, promoting inflammatory cells that suppress cancer while sparing normal tissue; another drives tumor expansion and tissue damage while dampening inflammation, suggesting a pathogenic role; and a third supports normal tissue maintenance but indirectly fuels cancer growth and may limit inflammatory cells via resource competition. These findings underscore the challenge of supporting normal tissue without inadvertently fueling cancer growth.
Oncolytic virotherapy uses viruses that selectively infect and lyse tumor cells while promoting antitumor immunity. Because viral spread, tumor growth, and immune-cell migration are spatially heterogeneous, purely temporal models may miss important treatment dynamics. We develop a reaction-diffusion delay model for spatial tumor virotherapy with a virus-induced cytotoxic T-lymphocyte (CTL) response, thereby incorporating tumor growth, infection, lysis, immune-mediated killing, diffusion, and delayed immune activation. We prove positivity, local well-posedness, and global boundedness under explicit sufficient conditions, and analyze spatially homogeneous equilibria and modal stability. Then, we extend the model with a numerical optimal-control formulation for viral administration and immune stimulation, thus minimizing tumor burden, treatment cost, and excessive CTL proliferation. Simulations indicate that tumor-virus-immune dynamics can remain spatially heterogeneous and that the computed optimal control schedules improve tumor suppression for the chosen parameter set.
The papaya mealybug, Paracoccus marginatus, has emerged as a formidable threat to global tropical agriculture, capable of inducing devastating yield losses through its invasive sap-sucking behavior. While conventional models often overlook environmental complexities, in this study, we introduced a sophisticated multi-seasonal mathematical framework designed to unravel the intricate interplay between mealybug population dynamics, fluctuating climatic conditions, and the persistence of off-season natural reservoirs. Sensitivity analysis highlighted how parameter influences shift across seasons, while our qualitative analysis revealed a dual-threshold mechanism, governed by the local offspring number $ \mathcal{N}_0 $ and the global stability threshold $ \mathcal{N}_g $, as the definitive driver of the system's long-term evolution. While $ \mathcal{N}_0 < 1 $ analytically ensures local asymptotic stability, our theoretical discussion suggested the existence of a conjectured regime of bistability within the threshold range $ \mathcal{N}_g < \mathcal{N}_0 < 1 $. This finding highlighted a critical regime where the success of eradication efforts is strictly contingent upon the initial infestation levels. Furthermore, by employing uniform persistence theory, we proved that the pest inevitably establishes a permanent foothold whenever $ \mathcal{N}_0 > 1 $. To mitigate these agricultural losses, we evaluated the efficacy of two distinct intervention frameworks: (ⅰ) Pulsed biological control via impulsive parasitoid releases and (ⅱ) a synergistic integrated pest management (IPM) strategy combining biopesticides with natural enemies. Our simulations demonstrated that while impulsive parasitoid releases alone achieved substantial suppression, reducing immature and mature female populations by 89.35% and 93.04%, respectively, and recovering 75.92% of papaya production, the integrated approach proved transformative. By synchronizing biopesticide applications with parasitoid pulses, mealybug populations were nearly decimated, with reduction rates reaching 99.70% for immatures and an exhaustive 99.90% for adults. Although this intensive suppression yielded a 44.92% increase in net productivity, its primary value lies in providing a robust, non-linear pathway toward total pest eradication, effectively breaking the cycle of reinfestation.
Portal hypertension is clinically defined by invasive hepatic venous pressure gradient (HVPG) thresholds, whereas routine assessment relies on non-invasive markers that are biologically heterogeneous and only indirectly related to portal pressure. We have developed a computational framework designed as a threshold-translation and scenario-exploration tool rather than a predictive or mechanistic model with three explicitly separated components: a data-driven empirical core, a literature-informed delayed dynamic layer, and a synthetic scenario module. Using HVPG-linked datasets, the empirical core has constructed a constrained latent burden score from liver stiffness, inverse platelet count, spleen diameter, inverse albumin, and bilirubin and has compared it with an equal-weight score. The constrained score has improved threshold discrimination more than continuous prediction at clinically relevant HVPG levels. A monotone burden-to-HVPG mapping has translated the latent burden axis into the clinically interpretable HVPG scale and has yielded cohort-specific burden thresholds. Leave-one-source-out (LOSO) technique shows that pooled burden learning is informative but not source-invariant, indicating limited transportability across cohorts. To examine delayed separation between latent burden evolution and visible pressure manifestation, we have introduced a delay differential equation model with literature-informed parameters. The resulting temporal gaps are illustrative scenario outputs and not patient-specific predictions. Overall, the framework provides a transparent, threshold-oriented computational approach for translating heterogeneous biomarkers into interpretable HVPG thresholds while linking data-based burden learning with scenario-based dynamic simulation.
Breast cancer is the most common cancer among women and represents 24.5% of all cancer cases worldwide. As there are few studies on the subject in Angola, it is particularly interesting to characterize the survival of women diagnosed with breast cancer in that country. The collected data set contains all diagnosed patients followed up at the Angolan Cancer Control Institute (IACC) between 2013 and 2022. However, due to the impact of COVID-19, the data set under analysis consists of the prepandemic period (2013 to 2019). The aim is to study the population diagnosed with cancer in the country, not only descriptively but also to check which factors influence the survival time of patients from diagnosis to death from breast cancer. To this end, various methods are applied to see which best describes the time until the event under study occurs. Namely, this study examines survival analysis models, beginning with the well-known Cox proportional hazards model. It then transitions to parametric models based on exponential and Weibull distributions and finally explores generalizations of these models that offer greater flexibility. To achieve this flexibility in the survival distribution, we adopt the proportional hazards framework proposed by Younes and Lachin but applying a new approach by Royston and Parmar. The results show that the median survival time from breast cancer in the observed women was 560 days. The variables that were revealed to be significant risk factors were age, stage of the disease, and body mass index. According to Akaike's criterion, the flexible proportional hazards model with one knot proved to be the most appropriate model for these data.
West Nile virus (WNV) is a mosquito-borne arbovirus with significant ecological and public health implications. Its transmission cycle involves avian hosts and mosquito vectors. Many factors, including host diversity and mosquito population dynamics are known to shape epidemic patterns. In this study, we extend previous work by incorporating multiple host types, horizontal transmission among hosts, and mosquito feeding preference into a WNV model. Using a system of ordinary differential equations, we analyze the impact of variable host competence, host abundance, host community structure, and mosquito biting preference on epidemic metrics. We derive an expression for the basic reproduction number in multihost systems and qualify the impact of less competent hosts on its value. Numerical simulations explore the impact of structural variations in the model on epidemic metrics and assess the potential for less competent hosts and mosquito feeding preference to dilute the epidemic. Our findings elucidate the influence of host heterogeneity, horizontal transmission in hosts, and mosquito biting preference on the severity and dynamics of a WNV epidemic.
In this paper, we introduce a new optimization algorithm that is well suited to solve parameter estimation problems that arise when inferring heterogeneous population dynamics. In these estimation problems, parameter estimation is complicated by the presence of two types of constraints: inequality constraints (e.g., non-negativity and boundedness of rates (so-called box-constraints)) and equality constraints that arise due to the need of the population fractions to sum to one. We call our new method cubic regularized Newton with affine scaling (CRNAS). In contrast to so-called first-order methods, which solely rely on the gradient of the objective function, our method utilizes the Hessian of the objective. As a result, it is able to focus on points that satisfy the second-order optimality conditions, as opposed to first-order methods that simply converge to critical points. This is an important feature in parameter estimation problems, where the objective function is often non-convex; as a result, there can be many critical points, which makes it nearly impossible to identify the global minimum. We use an affine scaling approach to handle a wide class of constraints, including equality constraints. We establish that CRNAS identifies a point that satisfies $ \epsilon $-approximate second-order optimality conditions within $ O(\epsilon^{-3/2}) $ iterations. Finally, we compare CRNAS with MATLAB's optimization solver fmincon on three different test problems. These test problems all feature mixtures of heterogeneous populations, a problem setting that CRNAS is particularly well-suited for. Our numerical simulations show that CRNAS has a favorable performance, thereby performing comparable, if not better than, fmincon in accuracy and computational cost for most of our examples.
This paper is concerned with elliptic equations satisfied by the mean first exit time of a stochastic process and higher moments. We prove an estimate for all moments of the first exit time in a cylindrical domain, using viscosity solutions. As a further result, we show the existence and the uniqueness of a more general fully nonlinear Dirichlet problem for partial trace equations, which can be associated to nonlinear diffusion.
In this paper, we develop and analyze a mathematical model for mosquito population control, incorporating the release of Wolbachia-infected male mosquitoes and the application of larvicides. Two complementary approaches are considered: An optimal control model with continuous-time control functions, and an impulsive control model accounting for periodic releases of Wolbachia-infected male mosquitoes and larvicide. The main objective is to minimize the population of fertilized females, which are responsible for the transmission of vector-borne diseases, while reducing the associated biological, social, and economic costs. Using the Pontryagin maximum principle, we characterize the optimal controls and demonstrate the existence of admissible solutions. Within the framework of the impulsive model, the existence and stability conditions for periodic solutions are rigorously derived, allowing the identification of critical thresholds for the larvicide concentration and the minimum density of Wolbachia-infected mosquitoes required to achieve a significant reduction in the target population. Numerical simulations illustrate the enhanced effectiveness of the combined intervention strategy, demonstrating both faster response times and a greater impact on population suppression. These findings emphasize the necessity of a scientifically grounded, optimized, and integrated approach in the design and implementation of vector control programs.
Considering that people usually take non-drug protective measures (making behavior changes), this paper proposes a new SEAIRS model by combining behavior changes during the spread of the COVID-19 epidemic. First, we prove the positivity and boundedness of the solution of the model. Furthermore, the existence and stability of the equilibrium points are discussed in three behavior scenarios $ (B_c = 0, \ B_c = 1, \ 0 < B_c < 1, $ where $ B_c $ represents the proportion of susceptible individuals ($ S $), exposed individuals ($ E $), and asymptomatic infected individuals ($ A $) who adopt preventive behavior changes). Finally, we illustrate the model's behaviour using COVID-19 data from Romania, and summarize some valuable results: (i) the spread of diseases can be effectively controlled by reducing the contact between susceptible, exposed, and infected individuals; (ii) increasing the proportion of behavioral changes can significantly reduce the number of infected individuals. The model suggests two main theoretical measures to promote behavior changes within the framework: one is to increase the return difference between the two behaviors by adjusting relevant parameters, and the other is to increase the value of the information function.
This paper studies an SI epidemic model with stochastic transmission rates of the form $ (\beta_t = \varphi(t)P_t:t\geq0) $, where $ \varphi(t) $ is a deterministic modulation function and $ P_t $ is a positive stochastic process. We show that the asymptotic behavior of the epidemic is determined by the integrated intensity process $ (H_t = \int_0^t \beta_s\, ds:t\geq0) $. We consider two stochastic models for $ (P_t:t\geq0) $: the bounded Jacobi process and the Cox-Ingersoll-Ross (CIR) process. Both preserve positivity, but differ in the support of their sample paths. In the non-modulated regime $ (\varphi\equiv1) $, the CIR framework allows explicit expressions for Laplace transforms and probabilistic bounds associated with the integrated intensity process. Additionally, we present numerical simulations in two regimes: the non-modulated case $ (\varphi(t) = 1) $ and the exponentially damped case $ (\varphi(t) = e^{-\alpha t}) $. The simulations show that the bounded and unbounded structures of the stochastic transmission processes produce different tail behaviors, particularly in high-volatility regimes.
We study a class of linear integral equations involving both a discrete delay and a bounded distributed delay. Such equations, as well as their non-linear extensions, arise in the mathematical modelling of biological systems and in control theory. The equations are discretised using quadrature-based methods, and the resulting discrete schemes are analysed with respect to their stability properties. Sufficient conditions are derived under which the discrete formulation preserves the stability characteristics of the underlying continuous problem.
Global sensitivity metrics are essential tools for assessing parameter importance in complex models, particularly when precise information about parameter values is unavailable. In many cases, such metrics are used to provide parameter rankings that allow for necessary dimension reduction in moderate-to-high dimensional systems. However, globally derived sensitivity results may obscure localized variability in parameter sensitivities, resulting in misleading conclusions about parameter importance and ensuing consequences for subsequent tasks such as model calibration and surrogate model construction. In this study, we illustrated how discrepancies between globally and locally based sensitivity information may arise for an emerging sensitivity metric based on active subspace methodology, as well as for other commonly used sensitivity techniques. In response, we outlined a framework that exploits the active subspace to evaluate the stability of parameter sensitivities over the admissible parameter space. This analysis allows one to determine the subregions of the parameter space in which a globally derived sensitivity metric may be considered representative of local behavior. The proposed framework was illustrated on a collection of simple examples for ease of visualization, as well as a variation of the Lotka-Volterra model used to study interactions between competing tumor cell lines, for which we demonstrated how these issues may be exacerbated in higher dimensions. Our findings suggest that globally derived sensitivity information should be treated with caution, and that incorporating analysis on local subregions may improve robustness and accuracy in downstream modeling tasks.
A network-based susceptible-infected-recovered (SIR) epidemic model is proposed to study the spread of infectious diseases, thereby incorporating vertical transmission and a saturated incidence rate. Additionally, it introduces double impulsive control strategies, including pulse vaccination and screening with treatment at distinct fixed intervals. Dynamical behaviors of the formulated model are analyzed using two types of transmission thresholds, namely $ R^0_{k_i} $ and $ \widehat{R^0_{k_i}} $. By applying the Floquet theorem and comparison principle, the system admits a disease-free periodic solution that is globally asymptotically stable if $ \max\limits_{i = 1, 2, \ldots, n}\widehat{R^0_{k_i}} < 1 $. The persistence of disease is confirmed from the uniform persistence of the Poincaré map when $ \frac{1}{1+\alpha}\max\limits_{i = 1, 2, \ldots, n}R^0_{k_i} > 1 $, where $ \alpha $ is the saturated coefficient in the saturation infection. Scenario studies are performed to numerically evaluate the impact of various parameters on the disease dynamics, and the effectiveness of double impulsive controls. It can be concluded that synthetical double impulsive controls are more efficient at eradicating the disease compared with only either of them.
Elevated introcular pressure (IOP) is a major risk factor for primary open angle glaucoma (POAG), the second leading cause of blindness worldwide. In this article, we investigate the relation between IOP increase and fluid-mechanical properties of the trabecular meshwork (TM), which is the main pathway of aqueous humor (AH) outflow in the human eye. TM is represented as an axisymmetric deformable biphasic porous medium (solid and fluid) with hydraulic permeability nonlinearly depending on the local AH pressure. Solving Darcy's law provides a TM hydraulic resistance (TMR) depending on the radial pressure drop, while TM stiffness is included multiplying the TMR by a shape function of TM Young's modulus constructed using postmortem measurements of human eye outflow facility. Simulations of AH flow based on an electric equivalent scheme of the eye indicate that TMR increases with TM stiffness, leading to a progressive increase of IOP until over the upper limit of the normal IOP range. The obtained results shed light on the impact of microscopic properties of the eye on its macroscopic function, and support the integration of experimental studies, mathematical modeling, and data analysis to develop an optimized patient-specific therapy to cure POAG.
The human immunodeficiency virus (HIV) epidemic in the United States has changed substantially since it was first identified in 1981; yet, progress toward ending the HIV epidemic targets remains uncertain. In this study, we examined the progress of the United States using HIV epidemic data from 1981 to 2025 and project trends through 2030 using mathematical transmission models. Two models were considered: A transmission model without pre-exposure prophylaxis (PrEP) and an extended model incorporating PrEP-related behavioral dynamics. Structural and practical identifiability analyses were used to assess whether model parameters could be reliably estimated from available surveillance data. Although both models were structurally identifiable under fixed assumptions, only the model without PrEP was practically identifiable with current surveillance data. We introduced the concept of virtual epidemics (VEs) and generated a collection of epidemic trajectories by repeatedly fitting the identifiable model to bootstrapped surveillance data. These VEs reproduced historical HIV incidence trends and yielded a range of plausible future outcomes. Our simulations suggested that, under current patterns of diagnosis, treatment, and prevention, the goal of reducing $ 90\% $ of the HIV epidemic in new infections by 2030 was unlikely to be met without additional intervention efforts.
