A system dynamics approach to model heat stress accumulation in dairy cows during a heatwave event

Climate change is expected to increase the number of heat wave events, leading to prolonged exposures to severe heat stress (HS) and the corresponding adverse effects on dairy cattle productivity. Modelling dairy cattle productivity under HS conditions is complicated because it requires comprehending the complexity, non-linearity, dynamicity, and delays in animal response. In this paper, we applied the System Dynamics methodology to understand the dynamics of animal response and system delays of observed milk yield (MY) in dairy cows under HS. Data on MY and temperature-humidity index were collected from a dairy cattle farm. Model development involved: (i) articulation of the problem, identification of the feedback mechanisms, and development of the dynamic hypothesis through a causal loop diagram; (ii) formulation of the quantitative model through a stock-and-flow structure; (iii) calibration of the model parameters; and (iv) analysis of results for individual cows. The model was successively evaluated with 20 cows in the case study farm, and the relevant parameters of their HS response were quantified with calibration. According to the evaluation of the results, the proposed model structure was able to capture the effect of HS for 11 cows with high accuracy with mean absolute percent error <5%, concordance correlation coefficient >0.6, and R² > 0.6, except for two cows (ID #13 and #20) with R² less than 0.6, implying that the rest of the nine animals do not exhibit heat-sensitive behaviour for the defined parameter space. The presented HS model considered non-linear feedback mechanisms as an attempt to help farmers and decision makers quantify the animal response to HS, predict MY under HS conditions, and distinguish the heat-sensitive cows from heat-tolerant cows at the farm level.