Dengue fever continues to be a major global health concern, particularly in tropical and subtropical regions. This research develops an updated fractional-order dengue transmission model that incorporates vector control methods with vertical transmission in mosquitoes. Memory effects are considered in the model formulation, which are examined using the Caputo fractional derivative. Through vertical transmission, Infected mosquitoes transmit the virus to their offspring, which keeps the infection active when humans are not available as hosts. Spraying insecticides together with biological control measures is part of vector control efforts that help assess how well the disease prevalence decreases. The Banach fixed-point theorem provides a basis to prove existence and uniqueness solutions. The mathematical model uses the basic reproduction number ($ \mathscr{R}_0$) to determine disease persistence, while stability conditions depend on equilibrium points. The investigation of local stability uses fractional-order stability theory together with a suitable Lyapunov function to establish global stability. The disease dynamics display changes through numerical results where fractional order variations combine with vector control measures. The simulation data demonstrates that vertical disease transmission functions as a crucial factor for maintaining dengue outbreaks, but strong vector control programs can significantly reduce spreading rates. The presented model functions as a foundation to establish optimal preventive strategies against dengue fever. The subsequent part of this work investigates optimal control models.

The concentrations of Pb(II), Cd(II), and Ni(II) ions in the groundwater (GW) of the Sargodha region of Pakistan are significantly higher than the WHO and

Hole-transport materials (HTMs) are crucial for controlling charge dynamics in perovskite solar cells, particularly at the interface and during electron recombination. Here, a series of benzodithiazole (BBT) cores, linked to side-arm triphenylamine (TPA) groups and possessing a donor-π-donor architecture, was designed through molecular engineering with various fluorine substitutions on the core. The optoelectronic characteristics of the designed HTMs were investigated using the B3LYP and CAM-B3LYP/6-31G** methods within the density functional theory (DFT)/time-dependent DFT (TD-DFT) framework. All materials displayed energy gaps of 2.60–2.63 eV and absorption maxima at ~400 nm. Frontier molecular orbital (FMO) investigations demonstrated an efficient intramolecular charge transfer (ICT)from the BBT core to TPA donor arms. The transition density matrix maps and the density of states further supported the significant charge transfer. The fluorinated-designed HTMs exhibited lower exciton binding energies (E_b = 0.3423–0.3472 eV), resulting in higher exciton dissociation rates and enhanced charge transfer. A benchmark analysis using Spiro-OMeTAD (2, 2, 7, 7-Tetrakis [N, N-di(4-methoxyphenyl)amino]-9, 9-spirobifluorene) as a standard in HTM studies demonstrated that the engineered HTMs exhibited enhanced hole-transport performance. Photovoltaic performance of the designed HTMs was evaluated using Solar Cell Capacitance Simulator in One Dimension (SCAPS-1D) device simulations. The optimized devices incorporating the designed HTM (BBT-F6) achieved a power conversion efficiency of up to 16%, outperforming the benchmark Spiro-OMeTAD under the same simulation conditions. These results indicate that structural modeling of organic HTMs with TPA donors can effectively tune their photovoltaic properties, making them promising candidates for efficient HTMs.