## 3 Related Work  
This section presents some models that provide hybrid solutions for the predictive modeling of glucose oscillation for T1D. Hybrid solutions usually combine mathematical modeling with data-driven techniques. In a literature search, [PERSON]. [8; 9; 10; 36] presented hybrid predictive models with PHs from 90 to 120 min. Nevertheless, for [16; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46], the prediction horizon (PH) varies from 30 to 60 min.  
In fact, Refs. [37; 41; 42] adopt neural network approaches that yield a PH of 60 min when dealing with nine, six and ten real patients, respectively; Ref. [38] adopts a combination of a compartment model and self-organizing map with twelve real patients, achieving a PH of 60 min; Refs. [39; 40] adopt a support vector machine approach tested with six and five real patients, respectively, both achieving a PH of 60 min. Moreover, Refs. [43; 44; 45; 46] achieved a PH of 30 min by adopting Bayesian inference, fuzzy logic, neural networks and a Kalman filter, respectively.  
For long-term PH, we can state that [PERSON] and colleagues et al., 2013 [8] adopted a multivariate regression approach to derive a predictive model for subcutaneous glucose concentration prediction in T1D individuals. The method was evaluated with a dataset composed of twenty-seven real T1D individuals and presented average prediction mean square errors of 5.21 mg/dL for 15 min, 6.03 mg/dL for 30 min, 7.14 mg/dL for 60 min and 7.62 mg/dL for 120 min PHs. [PERSON] and colleagues et al., 2019 [9] presented a glucose forecasting algorithm suited for long-term PHs. The algorithm is based on compartmental models for the HGIRS. It was evaluated with clinical data of ten real T1D individuals. For a 120 min PH, there was an improvement of 18.8% in the prediction accuracy measured with the root mean square error (RMSE), 17.9% in the A-region of error grid analysis (EGA) and 80.9% in the hypoglycaemia prediction calculated by the Matthews correlation coefficient. [PERSON], [PERSON] and [PERSON] et al., 2015 [10] presented a subspace-based linear multi-step predictor as a predictive model for short-term glucose oscillation. The model was evaluated with seven real T1D individuals and obtained a prediction error standard deviation of 58.06 mg/dL at 120 min. [PERSON] and colleagues et al., 2018 [36] combined physiological  
Figure 2: The piecewise polynomial for Lispro insulin (fast-acting) considering 0.16 U/kg concentration.  
models for HGIRS with grammatical evolution as a search-based technique to design a predictive model for short-term glucose oscillation. Considering the CEG, they achieved more than 96% of results falling inside regions A and B for 90 min.  
Since there are T1D individuals that feed at intervals greater than two hours, their results are not helpful for them. The proposal of the Tesseratus model is to extract the best features of each approach (physiology, data and multi-agent) in order to reach a longer PH at personalized intervals of four hours in the full daytime period and eight hours in the night period, keeping the MAE below 28 mg/dL in both periods and for all PHs. A discussion of the results is in Section 5.