The transmission dynamics of COVID-19 within and between age groups is studied using a mathematical model with direct and indirect transmission pathways. The model captures infections arising from contact with environmental pathogens and from exposed individuals, with an adjustment parameter introduced to account for reduced infectiousness associated with absence of severe symptoms. Effects of three potential drivers: heterogeneous contacts, differential susceptibility, and age-specific variations in infection severity on the age distribution of cases is investigated. Results of the model analysis show that differential susceptibility is the leading driver of the pattern of case distribution compared to heterogeneous contact and age-specific severity. It is also shown that initiating interventions 20 days earlier prevents approximately three times as many cases as those averted by mitigation implemented after 30 days. When heterogeneous contact is combined with differential susceptibility, the model predicts that early mitigation substantially reduces cases among adults by more than half but has limited impact on individuals younger than 20 years.
In this study, we introduce the two-parameter Pochhammer matrix function. Notably, we establish the (p, k) Pochhammer matrix symbol as a key new construct for our generalizations. Furthermore, we construct gamma and beta matrix functions of two parameters and prove properties similar to their classical counterparts. Additionally, we define the (p, k) Mittag-Leffler matrix function, exploring its fundamental properties, computation methods, and practical applications in solving systems of linear fractional differential equations.
Understanding the transmission dynamics of rabies among dogs is crucial for designing effective control strategies in endemic regions. In this study, we developed and analyzed two deterministic compartmental models. The SEI model captures the natural progression of rabies in the absence of intervention, while the SEIV model incorporates vaccination through pre-exposure prophylaxis (PrEP) for susceptible dogs and post-exposure prophylaxis (PEP) for exposed dogs. Analytical derivation of the basic reproduction number and stability analysis of disease-free and endemic equilibria (EE) were performed. Numerical simulations demonstrated that vaccination substantially reduces infection levels, with PrEP emerging as the dominant factor in controlling transmission. Vaccination thresholds indicate that coverage above 56% for combined PrEP and PEP at equal rates, or above 62% coverage of PrEP together with 30% or more coverage of PEP, or PrEP alone exceeding 70%, is sufficient to eliminate rabies in the dog population of Dhaka City, Bangladesh. Extending the SEIV model into an optimal control framework further revealed that time-dependent PrEP strategies effectively minimize infection, whereas PEP alone with feasible coverage is insufficient to eradicate the disease. Moreover, the cost-effectiveness analysis reveals that the only PrEP implementation is the most cost-effective strategy for vaccination-dependent (PrEP and PEP) suppression of dog rabies transmission. These findings highlight the critical role of vaccination, particularly PrEP, in achieving rabies elimination and support national and global efforts to end dog-mediated human rabies deaths by 2030.
Female genital schistosomiasis (FGS), caused by chronic infection with Schistosoma haematobium, represents a significant but neglected gynecological condition that affects approximately 56 million women in sub-Saharan Africa. This parasitic disease manifests itself through chronic inflammation and tissue damage in the female genital tract, leading to substantial morbidity and poor quality of life. Emerging epidemiological evidence suggests that FGS may function as an important cofactor in cervical carcinogenesis, potentially explaining the elevated burden of cervical cancer observed in schistosomiasis-endemic regions. However, the population level impact of this relationship and optimal intervention strategies remains poorly quantified. This study develops a compartmental mathematical model that integrates the transmission dynamics of schistosomiasis with human papilloma virus (HPV)–induced cervical carcinogenesis pathways. The model explicitly incorporates key biological mechanisms including chronic inflammation, immunomodulation, and synergistic interactions between FGS and HPV infection. The analytical derivation of the basic reproduction number yields R0=maxβSγ+τS+μ+βHPVγγ+τS+με+μ,βHPVε+μ, with the bifurcation analysis confirming a forward transcritical bifurcation at R0=1 (coefficients a<0 and b>0). This establishes R0<1 as necessary and sufficient for the elimination of the disease, without backward bifurcation complications. Our findings demonstrate that FGS contributes substantially to cervical cancer burden, with population attributable fraction (PAF) estimates ranging from 20% to 30% in high endemic settings. Cost-effectiveness analysis revealed that integrated interventions of mass drug administration (MDA), HPV vaccination, and cervical screening dominate vertical approaches, with incremental cost-effectiveness ratios (ICERs) of $172 per disability-adjusted living years averted from the model output. Sensitivity analysis identified the FGS risk ratio (ρ) as the most influential parameter, highlighting the critical need for better epidemiological characterization of this relationship. The model provides a robust platform for policy planning and resource allocation, demonstrating that coordinated control strategies addressing both neglected tropical diseases and noncommunicable diseases offer substantial synergistic benefits in reducing the dual burden of FGS and cervical cancer in endemic populations.
The Zika virus exhibits complex transmission dynamics involving vector-borne, sexual, and vertical pathways, which complicates the design of effective control strategies. In this work, we develop an integrated SICR–SI mathematical model coupling human and mosquito populations, incorporating Wolbachia-based biocontrol, sexual prevention, and vector control as intervention strategies. The model parameters are calibrated using epidemiological time-series data from seven Pacific island archipelagos, and the basic reproduction number R0 is analytically derived. Our results show that Wolbachia substantially reduces the vector component of transmission but cannot eliminate Zika in the presence of sexual transmission, which maintains a residual epidemic risk. We demonstrate that combining Wolbachia releases with sexual prevention yields a synergistic reduction in incidence greater than the sum of their individual effects. Using optimal control theory, we identify time-dependent intervention strategies that minimize both infection burden and implementation costs. A global sensitivity analysis (Sobol indices) highlights the dominant influence of mosquito-related parameters and Wolbachia coverage on epidemic outcomes. Overall, this study underscores the necessity of multitarget and coordinated intervention strategies to effectively reduce Zika transmission and its severe neurological complications.
This review article comprehensively analyzes recent developments in the generalization of special functions (SFs) and polynomials via various fractional calculus operators (FCOs), focusing on the analytical properties and applications of extended Hurwitz–Lerch zeta, Wright, and hypergeometric functions. Additionally, it explores the formulation of Appell-type matrix polynomials and novel solutions for generalized fractional kinetic equations, highlighting the effectiveness of integral transformation techniques in applied analysis and theoretical physics.
In this work, we consider a class of singularly perturbed differential-difference equations with small shift parameters in the convection and reaction terms, which frequently arise in applied mathematics and engineering. The presence of a small diffusion parameter ε,0<ε≪1 causes the solution of the considered problem to exhibit steep gradients (boundary layers), making classical numerical methods ineffective. To address this challenge, we formulate and analyze a fitted numerical scheme, employing the implicit Euler method in time and a midpoint upwind finite difference approach in space on uniform meshes. Stability and convergence analyses confirm second-order accuracy in both directions after Richardson extrapolation. Numerical experiments validate the theoretical results and demonstrate that the proposed method outperforms several existing methods in the literature.
This paper investigates the application of β-open sets to the convergence analysis of nonautonomous evolution equations governed by maximal monotone operators in Hilbert spaces. β-open sets are a class of generalized open sets introduced by Njåstad (1965), which coincides with the class of semiopen sets by Levine (1963). We first examine whether the properties of β-open sets, which form a generalized topology (not a classical topology), can offer a more flexible framework for studying trajectory convergence. And then we discuss potential advantages in relaxing certain coercivity conditions in contrast with analyses in standard metric or weak topologies, while addressing the non-Hausdorff nature and limited intersection closure of β-open sets. Examples from optimization problems (variational inequalities and sparse regression) and numerical insights from image denoising applications are utilized to illustrate the benefits of the approach. The paper highlights key challenges and outlines directions for further theoretical and computational development.
This article aims to present a new fixed point (FP) result for interpolative Kannan type and Ćirić-Reich-Rus type cyclic contractions (CRRTCCs) in dislocated quasi-rectangular b-metric spaces. We go through rigorous steps to prove the existence of a unique FP for the stated mapping in the setting of dislocated quasi-rectangular b-metric spaces. Our results generalize recent and related findings in literature. We provided a nontrivial example that justifies our findings. We also demonstrate the application of our result Theorem 3 on the existence of a unique solution for a nonlinear Fredholm integral equation. MSC2020 Classification 47H10, 54H25.
To satisfy the power needs of human beings without affecting the environment, scientists have been working on the efficient practices of renewable energy sources such as solar, water, and wind. As a source of energy resources, solar radiation is preferred because of its unlimited availability and low ecological impact. Thus, this article examines the heat transfer of unsteady electrically conducting viscous nanofluid flowing over a stretchable cylindrical surface in the presence of solar radiation. The entropy generation is also analyzed with the velocity slip and convective heat transfer boundary conditions. Considering Beer’s law for representing solar radiation, the horizontal cylindrical surface for nanofluid flow, and solving the model by the homotopy analysis method (HAM) can be the novelty of this study. The governing nonlinear partial differential equations (PDEs) are transformed into systems of higher-order nonlinear ordinary differential equations (ODEs) using appropriate similarity transformations. These ODEs are then solved via the HAM, applying the BVPh2.0 package on Mathematica 12.1. Comparisons with previously published studies confirm the validity of the method and highlight its consistency. The results reveal that the presence of a magnetic field interaction slows down the flow while increasing both local skin friction and the temperature of the nanofluid. Solar radiation and the Eckert and Biot numbers enhance the nanofluid’s temperature, whereas the Prandtl number and the unsteady parameter do not. Variations in temperature and velocity slip are found to reduce entropy generation. When the magnetic field interaction increased by 0.2, the local Nusselt number decreased by 0.1%, whereas the local skin friction rose by 6%. However, both the local Nusselt number and skin friction rose by 0.3% when the curvature parameter increased by 0.2. The findings demonstrate that the flow of nanofluid can be used to transfer heat from solar, which has practical applications in cooking, water heating, and electricity generation. Therefore, the global demand for energy can be partly met by harnessing solar energy effectively.
The recent resurgence of monkeypox highlights the urgent need for a deeper understanding of its transmission dynamics and effective intervention strategies. This study develops a nonlinear SEIR‐type model that integrates vaccination, treatment, and the impact of infective immigrants to assess monkeypox spread, especially under conditions of regional mobility. Real epidemiological data from Nigeria (2022–2023) are used to calibrate the model, which is shown to be mathematically well‐posed with positive, unique, and bounded solutions. Analytical results demonstrate that the disease‐free equilibrium is locally and globally stable when the basic reproduction number , and that an endemic state arises when . Sensitivity analysis identifies key parameters influencing transmission, notably contact rate, vaccine efficacy, and immigration. The model further incorporates time‐dependent control strategies for vaccination and treatment. Simulations using the Forward‐Backward Sweep Algorithm and fourth‐order Runge–Kutta method reveal that combining high vaccine coverage with timely treatment substantially reduces infection levels and shortens the duration of outbreaks. A cost‐effectiveness analysis based on the Incremental cost‐effectiveness ratio (ICER) confirms that implementing both vaccination and treatment is the most efficient and impactful strategy. These findings provide critical insights to guide public health policy, emphasizing the importance of proactive vaccination campaigns, efficient treatment protocols, and transboundary surveillance to curb monkeypox transmission. MSC2020 Classification: 92D30, 37N25, 34D20, 92B05, 92D25
We consider an advection-diffusion equation involving a fractional Laplace operator of order s ∈]0; 1]∖{1/2}. Using a combination of fractional left and right Riemann–Liouville derivatives of order 2 s to approximate the fractional Laplace operator, we construct a numerical scheme using the Crank–Nicolson method. Using the Crank–Nicolson scheme, we succeeded in putting the numerical scheme of the problem under consideration in the form of a strictly and diagonally dominant positive definite matrix. This has allowed us to prove that the numerical scheme is stable and converges to first order in time and space for s ∈]0; 1]∖{1/2}. Numerical tests are performed to illustrate the results. MSC2020 Classification : 35R11; 35S15; 65M12.
Rabies remains a significant public health concern, particularly in regions with high dog-mediated transmission, and understanding its dynamics is crucial for effective control strategies. This study investigates the transmission dynamics of rabies by developing a deterministic human-dog model extended to fractional-order derivatives, incorporating three operators: Caputo, Caputo–Fabrizio (CF), and Atangana–Baleanu–Caputo (ABC), to capture memory and hereditary effects. Model parameters were estimated from field data using the Markov chain Monte Carlo (MCMC) method, and the effective reproduction number, , was derived via a graph-theory approach. Mathematical analysis establishes the positivity, boundedness, and stability of solutions. Comparative simulations indicate that fractional-order models capture slower disease progression compared to classical integer-order systems, with the ABC operator producing the most conservative epidemic projections, reflecting realistic epidemic inertia. The study highlights the critical impact of vaccination, culling, and postexposure prophylaxis (PEP) in controlling rabies. The novelty of this work lies in the comprehensive comparison of different fractional-order operators within the same modeling framework, providing new insights into the role of memory effects in rabies transmission and guiding more effective intervention strategies.
