Mathematical study of the influence of canine distemper virus on tigers: an eco-epidemic dynamics with incubation delay

The decreasing tiger population in the world ecosystem is a threat to nature conservation. Canine distemper virus (CDV) is a deadly virus found in the tiger worldwide, one of the vital causes of their extinction. This paper figure outs the influence of CDV on tiger populations. We have developed and studied a delayed eco-epidemiological tiger-dog/wild carnivores predator-prey model with CDV infection in tiger and dog/wild carnivores considering incubation delay τ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau$$\end{document} for CDV infected dogs and wild carnivores. We studied the existence, boundedness, stability, and bifurcation of the solutions. Our analysis shows that the coexistence equilibrium is locally stable for all incubation delay τ>τ+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau >\tau ^+$$\end{document}. The system switches its stability as incubation delay crosses its critical value τ=τ+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau =\tau ^+$$\end{document}, perceives oscillations, and Hopf bifurcation occurs in the system for all τ<τ+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau <\tau ^+$$\end{document}. Further, the disease-free equilibrium also shows Hopf bifurcation for predator’s mortality rate threshold value μ2=μ2∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu _2=\mu _2^*$$\end{document}. We have performed a sensitivity analysis and identified the impact of the system’s parameters on reproduction number through their sensitivity indices. Finally, numerical simulation verifies the analytical finding that the significant incubation delay causes stability in the system. We can get a disease-free environment and save tigers by regulating the predation rate of healthy prey(dog/wild carnivores).