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

Praveen Agarwal, Ram Singh and Attiq ul Rehman

Chaos, Solitons & Fractals, 2021, vol. 143, issue C

Abstract: 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 R0 is investigated and calculated by next-generation technique. It’s also shows that if basic reproduction number R0<1, the disease-free equilibrium(DFE) is locally asymptotically stable(LAS) and if R0>1 then, the DFE is unstable. It’s also found that the fractional-order α also depends upon R0. Therefore, if fractional-order α=1 and R0>1, then dengue fever model doesn’t show Hopf-type bifurcation. Further, it’s also worth mentioning that although R0<1, the DFE E0 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.

Keywords: Hybrid mathematical model; Dengue transmission; Relapse; Memory; Hopf-type bifurcation (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:143:y:2021:i:c:s0960077920309553

DOI: 10.1016/j.chaos.2020.110564

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