Related Experiment Video
Updated: Sep 10, 2025

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
Published on: December 9, 2015
Deterministic and fractional-order modeling of measles dynamics with harmonic mean incidence rate and quarantine
Rehan Khan1, Ioan-Lucian Popa2,3, Emad A A Ismail4
1Department of Mathematics, University of Peshawar, Peshawar, 25000, Pakistan.
Abstract:
A novel mathematical model which explores the transmission dynamics of infectious diseases integrating nonlinear incidence and quarantine measures is presented in this study. Five different compartments: susceptible, latent, infectious, quarantined and recovered individuals presents total population. Saturation effects in disease transmission are modeled through a nonlinear infection rate while quarantine and recovery processes are explicitly incorporated. Parameters are estimated using a genetic algorithm based on cumulative monthly case data for measles in Indonesia. The basic reproduction number is derived to assess the potential for outbreak persistence. Stability analysis of the equilibrium states is conducted, and sensitivity analysis identifies key parameters influencing disease spread. Furthermore, the model is extended using Atangana-Baleanu Caputo (ABC) fractional derivative to explore memory-dependent effects in disease dynamics. Numerical simulations illustrate how fractional-order values impact infection trajectories. The findings emphasize the importance of timely isolation and recovery in controlling outbreaks and suggest that fractional-order modeling can enhance understanding of long-term epidemic behavior.
More Related Videos
12:21A Mouse Model for the Transition of Streptococcus pneumoniae from Colonizer to Pathogen upon Viral Co-Infection Recapitulates Age-Exacerbated Illness
Published on: September 28, 2022
10:11Modeling The Lifecycle Of Ebola Virus Under Biosafety Level 2 Conditions With Virus-like Particles Containing Tetracistronic Minigenomes
Published on: September 27, 2014
Related Concept Videos
Steps in Outbreak Investigation
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
Mechanistic Models: Compartment Models in Individual and Population Analysis
Causality in Epidemiology
Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...
Statistical Methods for Analyzing Epidemiological Data