Taenia solium taeniasis and cysticercosis: extinction or outbreak

Taenia solium taeniasis and cysticercosis are neglected zoonotic diseases that affect human health and economies of developing countries. In this work, we formulate and analyze deterministic and continuous time Markov chain (CTMC) stochastic models to determine parameters that drive Taenia solium taeniasis and cysticercosis and the likelihood of their extinction. The basic reproduction number R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document} is computed by the next generation matrix approach, sensitivity index of each parameter in R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document} is derived by the normalized forward sensitivity index and the likelihood of diseases’ extinction is computed by the multitype branching process. The analysis shows that humans with Taenia solium taeniasis, infectious pork and Taenia solium eggs in the environment play an important role in the transmission of Taenia solium taeniasis and cysticercosis, and the model exhibits forward bifurcation at R0=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0=1$$\end{document}. This implies that R0<1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0<1$$\end{document} is a sufficient condition to eliminate Taenia solium taeniasis and cysticercosis. For CTMC model, analysis shows that the probability of Taenia solium taeniasis and cysticercosis extinction is high if the diseases emerge from humans with Taenia solium cysticercosis and there is an outbreak if the diseases emerge from either humans with Taenia solium taeniasis or infectious pork or Taenia solium eggs in the environment. To control Taenia solium taeniasis and cysticercosis, the intervention strategies should focus on improving hygiene and sanitation for reducing shedding rate of Taenia solium eggs in the environment, inspection of pork for reducing the rate of acquiring Taenia solium taeniasis and spraying of insecticides for killing Taenia solium eggs in the environment.