Giri, Sunil

Tuncer, Necibe

English

Embry-Riddle Aeronautical University

Backward Bifurcation in vector-borne model with directtransmission.Sunil Giri1 Necibe Tuncer21 Florida Atlantic University, 777 Glades Road, Boca Raton, FL, US, 33431sgiri2012@fau.edu2 Florida Atlantic University, 777 Glades Road, Boca Raton, FL, US, 33431ntuncer@fau.eduThis paper deals with the study of time since infection structured vector bornmodel with the direct transmission. The model is analyzed to investigate the dy-namical behaviour of the system. Analysis of the existence and stability of equi-libria reveals the existence of backward bifurcation i.e. where the disease-freeequilibrium(DFE) coexists with the endemic equilibrium(EE) when the reproduc-tion numberR0 is less than unity. This aspect shows that in order to control vectorborne disease, it is not sufficient to have reproduction number less than unity al-though necessary. Thus, the infection can persist in the population even if thereproduction number is less that unity. Numerical simulation is presented to seethe bifurcation behaviour in the model. By taking the reproduction number asthe bifurcation parameter, we find the system undergoes backward bifurcation atR0 = 1. Thus, the model has backward bifurcation and may have one or two pos-itive endemic equilibrium when R0 < 1 and unique positive endemic equilibriumwheneverR0 > 1.Keywords: Backward bifurcation, Reproduction Number, Endemic Equilibrium,[4] [3] [1] [2]References[1] L.-M. Cai, X.-Z. Li, and Z. Li. Dynamical behavior of an epidemic model fora vector-borne disease with direct transmission. Chaos, Solitons & Fractals,46:54–64, 2013.[2] M. Martcheva. An introduction to mathematical epidemiology, volume 61.Springer, 2015.[3] N. Tuncer, M. Marctheva, B. LaBarre, and S. Payoute. Structural and practicalidentifiability analysis of zika epidemiological models. Bulletin of mathemati-cal biology, 80(8):2209–2241, 2018.[4] J. S. Welker and M. Martcheva. A novel multi-scale immuno-epidemiologicalmodel of visceral leishmaniasis in dogs. BIOMATH, 8(1):1901026, 2019.

Backward Bifurcation in Vector-Borne Model with Direct Transmission

https://commons.erau.edu/cgi/viewcontent.cgi?article=1049&amp;context=searcde

Backward Bifurcation in Vector-Borne Model with Direct Transmission

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