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It has been shown that reversible and irreversible phase transitions of biogels can be represented by epidemic models. The irreversible chemical sol–gel transitions are modeled by the Susceptible-Exposed-Infected-Removed (SEIR) or Susceptible-Infected-Removed (SIR) epidemic systems whereas reversible physical gels are modeled by a modification of the Susceptible-Infected-Susceptible (SIS) system. Measured sol–gel and gel–sol transition data have been fitted to the solutions of the epidemic models, either by solving the differential equations directly (SIR and SEIR models) or by nonlinear regression (SIS model). The gel point is represented as the “critical point of sigmoid,” defined as the limit point of the locations of the extreme values of its derivatives. Then, the parameters of the sigmoidal curve representing the gelation process are used to predict the gel point and its relative position with respect to the transition point, that is, the maximum of the first derivative with respect to time. For chemical gels, the gel point is always located before the maximum of the first derivative and moves backward in time as the strength of the activation increases. For physical gels, the critical point for the sol–gel transition occurs before the maximum of the first derivative with respect to time, that is, it is located at the right of this maximum with respect to temperature. For gel–sol transitions, the critical point is close to the transition point; the critical point occurs after the maximum of the first derivative for low concentrations whereas the critical point occurs after the maximum of the first derivative for higher concentrations.

The temperature and concentration dependences of the transmission spectrum of an aqueous solution of agar are investigated. Measurements taken in the heating and cooling modes show strong thermal hysteresis in the spectral properties. Analysis of the results suggests that the formation of a gel network occurs in a much narrower temperature range than its collapse. The study of the temperature dependence of transmittance indicates that the association bispirals by cooling the solution and responsible for the formation of network occurs at temperature about $40^{\circ }$C. A breakdown of these associates by heating of the gel begins at $60^{\circ }$C and covers a wide temperature range. The gel point $T_g$ and the gel melting point $T_m$ increase with increasing polymer concentration, but for $T_m$ this dependence is stronger. Growth of turbidity (light scattering) of gel by increasing of agar concentration is due to the increasing of number and size of gel associates.

Thermal hysteresis and stability of agarose–water gelling systems were studied by the spectrophotometer for different concentrations at different temperatures. Gelation temperature depends on the concentration of agarose. With the increase in the concentration of agarose gelation temperature, strength of agarose increases too. With the increase in the concentration of polymer solvent–gel phase transition, gel melting happens at higher temperatures. The price of enthalpy was determined (150.0127 KC/mol). In gelation process, the phase separation is completed and in this process, the value of this $\mathrm{\Delta }t=t_{\mathrm{\text{melting}}}-t_{\mathrm{\text{gelation}}}$ equally increases.

A solid-like structure with a certain yield strength will be formed when the oil temperature goes below its gel point. The oil temperature should be kept above its gel point during the pipeline transportation. It is hard to predict the gel point for multi-component blend crude oil, since the gel point of each single kind of oil will affect that of the blend oil in varying degrees, and the influence of single oil property and mixing proportion on the gel point of the multi-component blend crude oil is quite complicated with nonlinear characteristics. Considering the calculation of gel point for blend crude oil with a variety of components and mixing proportions as a multiple non-linear regression analysis, a prediction model for blend oil gel point is obtained by applying support vector machine algorithm, and the prediction result is reliable with a good accuracy.