The accelerated spread of antibiotic resistance genes (ARG) in the environment occurs mainly through plasmid transfer facilitated via bacterial conjugation. To predict and efficiently counteract the problems associated with ARG transmission, it is important to estimate conjugation rates under different experimental conditions. The classical models typically used to estimate parameters for mating experiments, while pragmatic in calculating growth and plasmid transfer, often ignore processes such as the reduction in growth due to plasmid bearing costs and are non-inclusive of environmental influences like temperature effects. Here, we present a process based numerical model taking into account the fitness cost associated with plasmid carriage and temperature dependencies in vertical and horizontal gene transfer processes. Observations from liquid culture conjugation experiments using Escherichia coli and the plasmid pB10 were used to validate our proposed model. We present a comparison between the parameters estimated using the existing and the proposed model. Uncertainties in the estimated parameters were quantified using classical and advanced Bayesian methods. For our mating experiments, we found that at temperatures between 20 and 37 degrees C, the plasmid bearing costs reduced the growth rates by > 35%. The temperature dependency model of conjugation showed a good fit (mean absolute percentage error < 10%) independent of the bacteria and the plasmid under study. The proposed model simultaneously estimates growth and plasmid transfer rate constants for all three strains (donor, recipient, and transconjugant). Simultaneous estimation of growth and conjugation parameters is particularly useful to estimate the spread of ARG when one of the mating partners inhibits the growth of the other, which is common in multi-species mating or when the incurred plasmid costs are situation dependent (e.g., increased plasmid cost in a mating environment) as observed in this study. (c) 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).