Analysis and numerical solution of novel fractional model for dengue

Abstract

Infectious diseases are the major source of increasing death rate during recent years. Among the infectious diseases, dengue fever is disseminated in more than hundred countries, especially in tropical and subtropical regions. In this work, a novel fractional model is presented which describes the dynamics of dengue including human and vector (mosquitoes) population. The mathematical model of dengue transmission is important to understand the dynamical behavior of the disease. A compartmental model of the dengue transmission is composed of five compartments representing the human and mosquito dynamics. The model is solved by using Adams-Bashforth-Moulton technique. The simulated results are compared with four years (2011–2014) real time data of dengue cases in Lahore, Pakistan. The fractional model gives a better approximation for α = 0.8 as compared to α = 1. The reasonable range of fractional order is between α = 0.7 and α = 1. The stability analysis of the equilibria is presented. Moreover, the positivity of the solution is proved. Furthermore, the parametric study using the outbreak dengue data for Lahore is presented. On the basis of results, we conclude that the fractional order model is more suitable than integer order equations to evaluate the transmission of dengue disease. The present study plays an important role in studying the factors to remove the communicable diseases like dengue.

Keywords

• Fractional order
• SIR model
• Nonlinear differential equation
• Stability
• Adams-Basthforth-Moulton technique