Numerical solution of hybrid mathematical model of dengue transmission with relapse and memory via Adam-Bashforth-Moulton predictor-corrector scheme

In this paper, a novel hybrid compartmental model of the dengue transmission process is proposed and studied with memory and relapse between host-to-vector and vice versa. The memory and correlated learning system in the dengue models by using the fractional differential operators such as Riemann-Liouville and Caputo has been a fascinating area of research. A threshold parameter which is called basic reproduction number R-0 is investigated and calculated by next-generation technique. It's also shows that if basic reproduction number R-0 < 1, the disease-free equilibrium(DFE) is locally asymptotically stable(LAS) and if R-0 > 1 then, the DFE is unstable. It's also found that the fractional-order alpha also depends upon R-0. Therefore, if fractional-order alpha =1 and R-0 > 1, then dengue fever model doesn't show Hopf-type bifurcation. Further, it's also worth mentioning that although R-0 < 1, the DFE E-0 may not be always stable but it's necessary and the model shows a Hopf-type bifurcation. We employed the scheme of Adams-Bashforth-Moulton predictor-corrector to find an approximate the solution of the dengue model. The numerical simulation is carried out to validate the analytic solution. (C) 2020 Elsevier Ltd. All rights reserved.

Automated summary

This paper introduces a novel hybrid compartmental model of dengue transmission process with memory and relapse. The study focuses on the impact of basic reproduction number R-0 on stability and Hopf bifurcation in the dengue model.