The conventional drug discovery approach is an expensive and time-consuming process, but its limitations have been overcome with the help of mathematical modeling and computational drug design approaches. Previously, finding a small molecular candidate as a drug against a disease was very costly and required a long time to screen a compound against a specific target. The development of novel targets and small molecular candidates against different diseases including emerging and reemerging diseases remains a major concern and necessitates the development of novel therapeutic targets as well as drug candidates as early as possible. In this regard, computational and mathematical modeling approaches for drug development are advantageous due to their fastest predictive ability and cost-effectiveness features. Computer-aided drug design (CADD) techniques utilize different computer programs as well as mathematics formulas to comprehend the interaction of a target and drugs. Traditional methods to determine small-molecule candidates as a drug have several limitations, but CADD utilizes novel methods that require little time and accurately predict a compound against a specific disease with minimal cost. Therefore, this review aims to provide a brief insight into the mathematical modeling and computational approaches for identifying a novel target and small molecular candidates for curing a specific disease. The comprehensive review mainly focuses on biological target prediction, structure-based and ligand-based drug design methods, molecular docking, virtual screening, pharmacophore modeling, quantitative structure–activity relationship (QSAR) models, molecular dynamics simulation, and MM-GBSA/MM-PBSA approaches along with valuable database resources and tools for identifying novel targets and therapeutics against a disease. This review will help researchers in a way that may open the road for the development of effective drugs and preventative measures against a disease in the future as early as possible.

Dengue impacts 129 nations, threatens over 50% of the global population, and results in around 400 million illnesses annually. The purpose of this paper was to build the global stability and sensitivity analysis of a vector-host dengue mathematical model with compartments of symptomatic and hospitalized infected humans. Additionally, it aimed to assess the impact of the immunological response of vulnerable individuals, through the ingestion of natural foods, on the transmission of the disease. The solution's positivity and boundedness proved the model's mathematical well-posedness. To examine endemicity, the reproduction number was calculated using the next-generation technique. The Lyapunov function approach was employed to illustrate the model's global stability. Our mathematical discoveries were illustrated through numerical simulations of the dengue epidemic. The dynamical system sensitivity analysis suggests that the best way to control illness is to increase the immune system rate of susceptible hosts by consuming natural foods.

A global health hazard, dengue fever causes or contributes to the deaths of 10,000 people and 100 million cases of symptomatic cases every year in more than half of the globe. The goal of this work is to construct a compartmental vector-borne dengue model that takes into account the typical incidence connection between infected humans and susceptible vectors in order to examine the impact of model parameters that are within our control on the basic reproduction number. In order to determine the basic reproduction number \(R_0\), the next-generation matrix is used. The theoretical study reveals that disease-free equilibrium occurs as a locally asymptotically stable if \(R_0<1\). To measure the disease-free and endemic equilibrium points' global stability, LaSalle's concept is applied. The normalized forward sensitivity index methods show that the epidemic spread can reduce by increasing the rate of symptomatically infected humans to isolated infected humans and the rate of recovery of symptomatically infected humans.

The global outbreak of the monkeypox virus (Mpox) in 2022–2023, which affected over 100 countries, has underscored the urgent need for robust public health interventions and predictive modeling tools. In this study, we develop a novel mathematical model that captures the transmission dynamics of Mpox between human and rodent populations, incorporating both direct and environmental transmission pathways as well as the effects of vaccination. We prove the model's positivity and boundedness to ensure epidemiological feasibility. Using the next-generation matrix method, we derive the basic reproduction number and assess the local and global stability of both disease-free and endemic equilibria through Lyapunov-based techniques. Sensitivity analysis identifies critical parameters influencing Mpox spread and informs targeted intervention strategies. Numerical simulations illustrate how varying key parameters such as vaccination rates, recovery rates, and transmission pathways affect disease progression. The results emphasize that increasing vaccination coverage and enhancing recovery rates can significantly reduce disease burden. This model provides a comprehensive framework to support evidence-based public health decision-making for controlling future Mpox outbreaks.

Tilapia Lake Virus (TiLV) is a disease that affects tilapia fish, causing a high rate of sudden death at any stage of their growth. Unfortunately, there are currently no effective antiviral drugs or vaccines to control the progression of this disease. Researchers have discovered that the CRM1 protein plays a critical function in the development and spreading of animal viruses. By inhibiting CRM1, the virus’s spread in commercial fish farms can be suppressed. With this in mind, this study intended to identify potential antiviral drugs from two different tropical mangrove plants from tropical regions: Heritiera fomes and Ceriops candolleana . To identify promising compounds that target the CRM1 protein, a computer-aided drug discovery approach is employed containing molecular docking, ADME (absorption, distribution, metabolism and excretion) analysis, toxicity assessment as well as molecular dynamics (MD) simulation. To estimate binding affinities of all phytochemicals, molecular docking is used and the top three candidate compounds with the highest docking scores were selected, which are CID107876 (-8.3), CID12795736 (-8.2), and CID12303662 (-7.9). We also evaluated the ADME and toxicity properties of these compounds. Finally, molecular dynamics simulation was conducted to analyze the stability of the protein-ligand complex structures and confirm the suitability of these compounds. The computational study demonstrated that the phytochemicals found in H. fomes and C. candolleana could potentially serve as important inhibitors of TiLV, offering practical utility. However, further in vivo investigations are necessary to investigate the effectiveness of these compounds as antiviral drugs against the virus TiLV.

This research investigates the dynamics of higher-order nonlinear difference equations, specifically concentrating on seventh-order instances. Analytical solutions are obtained for particular equations, a formidable task owing to the absence of explicit mathematical techniques for their resolution. The qualitative characteristics of solutions, such as their stability, boundedness, and periodicity, are analysed by theoretical methods and numerical simulations. The results indicate that equilibrium points frequently lack local asymptotic stability, leading to intricate phenomena such as unbounded solutions and periodic attractors. These findings augment our understanding of nonlinear difference equations, offering significant implications for their use across various scientific fields.