Mathematical Analysis and Numerical Simulation of Lassa Fever Dynamics: A Fractional-Order Modeling Approach using Atangana–Baleanu Derivative in the Caputo Sense

Abstract

This repository contains the numerical implementation and simulation scripts for the research paper: "Fractional-Order Modeling of Lassa Fever Dynamics: Analyzing the Impact of Reservoir Vertical Transmission and Human Nosocomial Multipliers via the Atangana-Baleanu Operator". The project provides a computational framework to study the transmission dynamics of Lassa fever using the Atangana-Baleanu-Caputo (ABC) fractional derivative. Unlike traditional integer-order models, this approach captures the "memory effects" and crossover behaviors essential for modeling infectious diseases with long-term environmental and reservoir persistence. Key Features: Mathematical Framework: Implementation of an 8-compartment deterministic model $(\mathcal{S, E, I, R})$ for humans and $(\mathcal{U, V})$ for rodents. Fractional Dynamics: Numerical solutions using the fractional Adams-Bashforth-Moulton predictor-corrector scheme. Epidemiological Factors: Inclusion of vertical transmission in the rodent population and nosocomial (hospital-acquired) multipliers in the human population. Sensitivity & Control: Code for calculating the Basic Reproduction Number $(\mathcal{R}_{0})$ and performing sensitivity analysis to identify the most impactful intervention strategies. Data Calibration: The model is parameterized using NCDC epidemiological data spanning 2021–2026. Files Included: Lassa_ABC_Solver.m: The core script for the ABC fractional-order numerical integration. Sensitivity_Analysis.m: Scripts for PRCC and sensitivity index calculations. Optimal_Control_Sim.m: Evaluation of personal protection, treatment, and culling strategies. Plotting_Suite.m: Generates the epidemic curves and phase-space trajectories.