Moustafa El-Shahed

Asthma is one of the most prevalent chronic respiratory diseases worldwide, and environmental pollutants such as desert dust play a significant role in triggering respiratory sensitization and aggravating asthma symptoms. In this study, a mathematical model is proposed to investigate the dynamics of dust-induced asthma progression. The population is divided into unaware susceptible individuals, aware susceptible individuals, dust-sensitized individuals, and asthmatic individuals, while two additional variables describe dust concentration in the human population and the environment. Fundamental qualitative properties of the model, including positivity, boundedness, existence of equilibria, and stability conditions, are established. It is shown that the asthma-free equilibrium is locally and globally asymptotically stable whenever the dust-induced asthma threshold is below unity, whereas a unique asthma-persistent equilibrium exists when the dust-induced asthma threshold exceeds unity. To reduce the burden of asthma, an optimal control problem is formulated by incorporating three time-dependent interventions: awareness campaigns, medical intervention for dust-sensitized individuals, and environmental dust reduction. Pontryagin’s Maximum Principle is employed to characterize the optimal controls and derive the corresponding adjoint system. Numerical simulations, performed using the forward–backward sweep method, demonstrate that the proposed interventions significantly reduce the number of asthmatic individuals compared with the uncontrolled case. Furthermore, a cost-effectiveness analysis based on the Average Cost-Effectiveness Ratio (ACER) and Incremental Cost-Effectiveness Ratio (ICER) is conducted to compare seven intervention strategies. The results indicate that the medical intervention strategy is the most economically attractive option, while the combined strategy involving all controls achieves the largest reduction in asthma burden.

This paper develops an optimal control framework for a mechanical–structural model of bone remodeling that couples osteocytes, osteoblasts, and osteoclasts with bone density, incorporating porosity-dependent feedback mechanisms. To represent clinically relevant interventions, three bounded control functions are introduced: anabolic stimulation of osteoblast activity, anti-resorptive suppression of osteoclast-mediated resorption, and structural modulation of porosity feedback. The controlled system is shown to be mathematically well-posed, and the necessary optimality conditions are derived via Pontryagin’s Maximum Principle, leading to explicit characterizations of the optimal controls. The resulting state–adjoint system is solved numerically using a forward–backward sweep method. Numerical results demonstrate that the optimal intervention effectively suppresses osteoclast activity and drives the system toward higher, more stable bone density levels than the uncontrolled dynamics. In particular, the anti-resorptive control consistently plays the dominant role in shaping the optimal strategy. A cost-effectiveness analysis based on ACER, ICER, and the efficient frontier shows that strategies involving anti-resorptive inhibition achieve the greatest therapeutic gains at moderate cost, while additional controls yield only marginal improvements. Sensitivity analysis further indicates that parameters associated with osteoclast dynamics and bone formation have the strongest influence on density-related outcomes.

This paper formulates and analyzes a stochastic predator-prey model focusing on the elk–wolf dynamics. The mathematical framework is motivated by the Banff–Bow Valley ecosystem, where the elk population is categorized into urban and valley subgroups, both subject to wolf predation. We extend the deterministic interaction model into a system of stochastic differential equations to incorporate environmental fluctuations. The global existence and uniqueness of positive solutions are established, ensuring the biological realism of the model. By applying logarithmic Itô calculus and Lyapunov function techniques, we derive explicit extinction criteria and prove moment as well as ultimate boundedness properties of the populations. Moreover, we introduce a practical parameter-based stochastic threshold that characterizes predator persistence and stochastic permanence, highlighting qualitative differences between deterministic coexistence and noise-induced extinction. Finally, numerical simulations based on the Euler–Maruyama scheme are provided to illustrate the theoretical results and confirm the predicted long-term stochastic behaviors.

In this study, we develop a mathematical model to describe the transmission dynamics of the Respiratory Syncytial Virus (RSV), incorporating the coexistence of two distinct strains. The global stability of the disease-free and endemic equilibria is analyzed. Bifurcation analysis reveals the occurrence of a forward bifurcation. To control the spread of the infection, Pontryagin’s maximum principle is applied within the framework of optimal control theory, considering intervention strategies such as isolation, treatment, and vaccination. A detailed evaluation of the effectiveness of these control strategies is conducted for a specific population based on a nonlinear optimal control model. Moreover, a cost-effectiveness analysis is performed to identify the most economically viable intervention. The findings indicate that, among the studied interventions, isolation is the most cost-effective strategy for reducing RSV prevalence. The model is numerically solved using the fourth-order Runge–Kutta method, coupled with the forward–backward sweep algorithm, to assess the impact of various control combinations on the transmission dynamics of RSV.

This study presents a mathematical model to describe the transmission dynamics of the Hepatitis B Virus (HBV), accounting for two distinct viral strains. The basic reproduction number, R0, is derived using the next-generation matrix method, and three equilibrium points are identified. Stability analysis reveals that the disease-free equilibrium is locally asymptotically stable when R0 < 1, the first strain-free equilibrium is stable when R02 > R01, and the endemic equilibrium is stable when R0 > 1. An optimal control problem is then formulated to evaluate the effectiveness of two intervention strategies: vaccination and treatment. The objective is to minimize infection levels and reduce economic burden. Using Pontryagin's Maximum Principle, the necessary conditions for optimal control are established within a deterministic framework. Numerical simulations, implemented in MATLAB, support the theoretical findings and demonstrate the impact of the proposed controls. Cost-effectiveness analysis indicates that treatment is the most economically efficient strategy. The model offers practical insights for HBV-endemic regions, particularly those with constrained healthcare resources.

In this study, we formulate and analyze a deterministic mathematical model describing the transmission dynamics of pneumonia. A comprehensive stability analysis is conducted for both the disease-free and endemic equilibrium points. The disease-free equilibrium is locally and globally asymptotically stable when the basic reproduction number R₀ < 1, while the endemic equilibrium is locally and globally asymptotically stable when R₀ > 1. To evaluate effective intervention strategies, an optimal control problem is formulated by introducing time-dependent control variables representing awareness campaigns, screening of carriers, and treatment of infected individuals. Applying Pontryagin’s Maximum Principle, the simulation results confirm the effectiveness of the proposed control strategies in reducing the number of infections and mitigating the overall disease burden. The findings offer valuable insights into the control of pneumonia and highlight the potential impact of strategic public health interventions.

This study presents a mathematical model to describe the transmission dynamics of asthma, explicitly accounting for the impact of dust waves and airborne particulate matter in the environment, recognized as key triggers of asthma exacerbations. The model incorporates a single endemic equilibrium point, which is shown to be locally asymptotically stable. To mitigate the burden of asthma, we employed the Pontryagin Maximum Principle within an optimal control framework, incorporating three time-dependent intervention strategies: vaccination, treatment, and avoidance of environmental triggers such as dust exposure. The model was numerically solved using the fourth-order Runge–Kutta method in conjunction with a forward–backward sweep algorithm to investigate the effects of various control combinations on the prevalence of asthma. Additionally, a comprehensive cost-effectiveness analysis was conducted to evaluate the economic viability of each strategy. The results indicate that the combined application of vaccination and treatment is the most cost-effective approach among the strategies analyzed, significantly reducing the number of asthma cases at minimal cost. All simulations and numerical experiments were performed to validate the theoretical findings and quantify the effectiveness of the proposed interventions under realistic environmental conditions driven by dust activity. The model highlights the importance of integrated medical and environmental control policies in mitigating asthma outbreaks, particularly in regions frequently exposed to dust storms.

In this paper, a fractional-order eco-epidemiological model with two disease strains in the predator population incorporating harvesting is formulated and analyzed. The model assumes that the population is divided into a prey population, a susceptible predator population, a predator population infected by the first disease, and a predator population infected by the second disease. A mathematical analysis and numerical simulations are performed to explain the dynamics and properties of the proposed fractional-order eco-epidemiological model. The positivity, boundedness, existence, and uniqueness of the solutions are examined. The basic reproduction number and some sufficient conditions for the existence of four equilibrium points are obtained. In addition, some sufficient conditions are proposed to ensure the local and global asymptotic stability of the equilibrium points. Theoretical results are illustrated through numerical simulations, which also highlight the effect of the fractional order.

The red palm weevil (Rhynchophorus ferrugineus) is a highly destructive pest, causing severe damage to palm trees and significantly reducing their productivity. This paper aims to develop and analyze a mathematical model that captures the interactions between palm trees, Rhynchophorus ferrugineus, and entomopathogenic nematodes as a means of integrated control. We identify the equilibrium points of the system and perform a stability analysis to assess the system’s behavior. Additionally, we design a linear quadratic regulator (LQR) to limit the spread of the red palm weevil within a locally linearized framework. The feedback control law, which is both straightforward and immediately implementable, is employed to avoid the need for complex cost calculations, thus simplifying the solution to the optimal control problem. Numerical simulations demonstrate that the proposed control strategy is effective in reducing the number of infected palm trees. The results indicate that increasing the population of entomopathogenic nematodes can significantly decrease the red palm weevil population, offering a promising approach to mitigating this pest’s impact.