The impact of time delay on the transmission of Japanese encephalitis model without vaccination

• Baniya, Vinod ^[1] ; Keval, Ram ^[1]
  1. [1] University of Technology

     University of Technology

     Rusia

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 40, Nº. 6, 2021, págs. 1367-1410
• Idioma: inglés
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• Resumen

  • 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.