Abstract
In this manuscript, the influence of time delay in the transmission of Japanese encephalitis without vaccination model has been studied. The time delay is because of the existence of an incubation period during which the Japanese encephalitis virus reproduces enough in the mosquitoes with the goal that it tends to be transmitted by the mosquitoes to people. The motivation behind this manuscript is to assess the influence of the time delay it takes to infect susceptible human populations after interacting with infected mosquitoes. The steadystate and the threshold value R0 of the delay model were resolved. This value assists with setting up the circumstance that ensures the asymptotic stability of relating equilibrium points. Utilizing the delay as a bifurcation parameter, we built up the circumstance for the presence of a Hopf bifurcation. Moreover, we infer an express equation to decide the stability and direction of Hopf bifurcation at endemic equilibrium by using center manifold theory and normal structure strategy. It has been seen that delay plays a vital role in stability exchanging. Furthermore, the presence of Hopf bifurcation is affected by larger values of virus transmission rate from an infected mosquito to susceptible individuals and the natural mortality of humans in a model. Finally, to understand some analytical outcomes, the delay framework is simulated numerically.
Highlights
In the current year, the incidence of Japanese encephalitis (JE) has risen significantly across the world
We investigated the impact of time delay on the dynamics of the Japanese encephalitis system in this study
500 1000 1500 2000 2500 3000 Time (t) tion outcomes show that the time delay incredibly influences the dynamics of the framework
Summary
The incidence of Japanese encephalitis (JE) has risen significantly across the world. Kumar et al, [23] have constructed the SIR pandemic model with the deterministic time-delayed system In his work they have taken the Holling type III function as a treatment rate and nonlinear functional as the incidence rate of infection, Hopf bifurcation occurs in his system. Goel et al, [20] have constructed and analyzed a SIR epidemic framework with time-delayed, saturated functional-type treatment rate and Beddington–DeAngelis-type incidence rate In his work, they have derived the circumstances for the occurrence of backward bifurcation and Hopf bifurcation. The main point of this manuscript is to build up a compartmental framework with a time delay without vaccination that makes susceptible humans infectious after interaction with infected mosquitoes.
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