Mathematical validation of cleaning symbiosis between Macrobrachium lamarrei and Labeo rohita as an effective bio-control method against Argulus bengalensis

Argulosis, caused by the crustacean (Order- Branchiura) ectoparasite Argulus spp., poses a significant economic loss in global aquaculture. Recently, a potential bio-control strategy against argulosis was proposed, which involved three taxonomically separate organisms in cohabitation: the client fish Labeo rohita (F), the cleaner prawn Macrobrachium lamarrei (P), and the parasite Argulus bengalensis (A). However, the effectiveness of the association was only proven in a microcosm experiment; no field application was performed. Therefore, to fill this gap, the present interpretation has been directed towards a mathematical validation of this three-species association for its successful large-scale field application. A conceptual model is proposed with the three state variables F, P and A for this purpose. The parametric values, used to formulate the mathematical model, were obtained from the microcosm experiment, field observation and calibration. The experiment was conducted in microcosm maintaining the client, cleaner and parasite ratio as 1:5:100 for acquiring the values of the coefficient of interaction ($\alpha$) between the fish and Argulus and the maximum predation rate ($\gamma$) of prawn. However, an ‘ideal’ condition was also created by maintaining this ratio as 1:1:100 to obtain half saturation constant of predation ($h$). The values of intrinsic growth rate (r) of fish and carrying capacity (K) of the aquaculture system were determined according to a particular polyculture system where this specific ratio was 1:2:50. The Holling type III equation was used to solve this mathematical model equation. The result demonstrates that the predation rate of the prawn species inversely influences the Argulus population and directly influences the prawn population. Therefore, M. lamarrei can be used as an additional species in composite fish culture to regulate Argulus load in aquaculture systems without compromising the balance of an ecosystem. Moreover, this study is a novel work that considers dual role of the three interacting species for model formation and analysis. So, the current study is important in both the sectors of aquaculture and ecology.