Modeling transport of antibiotic resistant bacteria in aquatic environment using stochastic differential equations

Contaminated sites are recognized as the “hotspot” for the development and spread of antibiotic resistance in environmental bacteria. It is very challenging to understand mechanism of development of antibiotic resistance in polluted environment in the presence of different anthropogenic pollutants. Uncertainties in the environmental processes adds complexity to the development of resistance. This study attempts to develop mathematical model by using stochastic partial differential equations for the transport of fluoroquinolone and its resistant bacteria in riverine environment. Poisson’s process is assumed for the diffusion approximation in the stochastic partial differential equations (SPDE). Sensitive analysis is performed to evaluate the parameters and variables for their influence over the model outcome. Based on their sensitivity, the model parameters and variables are chosen and classified into environmental, demographic, and anthropogenic categories to investigate the sources of stochasticity. Stochastic partial differential equations are formulated for the state variables in the model. This SPDE model is then applied to the 100 km stretch of river Musi (South India) and simulations are carried out to assess the impact of stochasticity in model variables on the resistant bacteria population in sediments. By employing the stochasticity in model variables and parameters we came to know that environmental and anthropogenic variations are not able to affect the resistance dynamics at all. Demographic variations are able to affect the distribution of resistant bacteria population uniformly with standard deviation between 0.087 and 0.084, however, is not significant to have any biological relevance to it. The outcome of the present study is helpful in simplifying the model for practical applications. This study is an ongoing effort to improve the model for the transport of antibiotics and transport of antibiotic resistant bacteria in polluted river. There is a wide gap between the knowledge of stochastic resistant bacterial growth dynamics and the knowledge of transport of antibiotic resistance in polluted aquatic environment, this study is one step towards filling up that gap.