Bulletin of Mathematical Biology (2006) 68: 1293–1314 DOI 10.1007/s11538-006-9076-x ORIGINAL ARTICLE A Process-Based Mathematical Model on Methane Production with Emission Indices for Control A. Chakraborty a,∗ , D. K. Bhattacharaya b a 4145 Batchelor Hall, Center for Conservation Biology, University of California, Riverside, USA b Department of Pure Mathematics, University of Calcutta, 35 Ballygange Circular Road, Kolkata 19, West Bengal, India Received: 10 August 2005 / Accepted: 18 January 2006 / Published online: 22 April 2006 C  Society for Mathematical Biology 2006 Abstract In this paper, a process-based mathematical model is developed for the production of methane through biodegradation. It is a three-dimensional model given by ordinary differential equations. The results of the analysis of the model are interpreted through three emission indices, which are introduced for the first time. The estimation of either one or all of them can interpret the feasibility of the equilibrium and the long-term emission tendency of methane. The vulnerabil- ity of the methane production process with respect to soil temperature effects in methanogenic phase has been discussed and a feasible condition within a specified temperature range has defined for the nonvulnerability of the methane produc- tion process and also it has shown that under the same condition, zero-emission process of methane will be nonvulnerable with respect to the soil temperature ef- fects in methanogenic phase. Lastly, condition for zero emission of methane is also obtained and it is interpreted through the emission indices. Keywords Stability · Basin of attraction · Methanogenesis · Nonvulnerability · Monod type-2 kinetics · Liapunov function 1. Introduction Methane is one of the principal greenhouse gases, which affect earth’s temperature and climate systems driven by mainly CO 2 and N 2 O. During the last two centuries, methane concentration in the atmosphere has been doubled—its amount in the preindustrial times was 700 parts per billion by volume (ppbv)— its amount in 1997 was found to be 1.730 ppbv (EPA, September 1999). Since GWP (Global Warming Potential) of methane is 21, so it is very much urgent to estimate methane emission ∗ Corresponding author. E-mail address: amitc@ucr.edu (A. Chakraborty).