Analysis of time delayed Rabies model in human and dog populations with controls

Abstract

Rabies is a fatal zoonotic disease caused by a virus through bites or saliva of an infected animal. Dogs are the main reservoir of rabies and responsible for most cases in humans worldwide. In this article, a delay differential equations model for assessing the effects of controls and time delay as incubation period on the transmission dynamics of rabies in human and dog populations is formulated and analyzed. Analysis from the model show that there is a locally and globally asymptotic stable disease-free equilibrium whenever a certain epidemiological threshold, the control reproduction number \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {R}_v$$\\end{document}Rv, is less than unity. Furthermore, the model has a unique endemic equilibrium when \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {R}_v$$\\end{document}Rv exceed unity which is also locally and globally asymptotically stable for all delays. Time delay is found to have influence on the endemicity of rabies. Vaccination of humans and dogs coupled with annual crop of puppies are imposed to curtail the spread of rabies in the populations. Sensitivity analysis on the number of infected humans and dogs revealed that increasing dog vaccination rate and decreasing annual birth of puppies are more effective in human populations. However in dog populations, the vaccination and birth control of puppies, have equal effective measures for rabies control. Numerical experiments are conducted to illustrate the theoretical results and control strategies.