A computer-implemented method for determining a cycle threshold for a PCR amplification curve, the method comprising: receiving a data set for a plurality of biological samples for a PCR amplification reaction, wherein the data set includes a plurality of amplification curves, each amplification curve associated with a biological sample of the plurality of biological samples; performing a constrained nonlinear optimization comprising a fit of each of the plurality of amplification curves to a modeled amplification curve to determine a best-fit set of parameters for a modeled efficiency curve and the modeled amplification curve, and wherein the best-fit set of parameters are used to create the modeled efficiency curve and the modeled amplification curve for each of the plurality of amplification curves; and determining a relative cycle threshold value, C RT, for each biological sample by using the modeled efficiency curve and the modeled amplification curve, wherein the constrained nonlinear optimization is a constrained non-linear parameter optimization, wherein the best-fit set of parameters for the modeled efficiency curve and the modeled amplification curve comprises three parameters being a curve shift parameter, a curve bend parameter, and a curve shift adjustment parameter, and comprises additionally two parameters being an amplification curve rising baseline slope parameter and an amplification curve relative amplification parameter for the modeled amplification curve, and said modeled efficiency curve is of a 3-parameter efficiency model using said three parameters and said modeled amplification curve is of a 5-parameter amplification model using said three parameters and said additionally two parameters, wherein using the modeled efficiency curve and the modeled amplification curve to determine the C RT value for each biological sample comprises: - using a selected efficiency value on the respective modeled efficiency curve to determine a reference threshold value on the respective modeled amplification curve; - multiplying the reference threshold value by a relative threshold fraction to determine a relative threshold fraction value on the respective modeled amplification curve to identify an unadjusted C RT; and - using a cycle adjustment factor to adjust the unadjusted C RT to obtain the C RT, wherein determining the C RT is based on the efficiency value being selected from between about 0.15 to 0.5, and wherein the relative threshold fraction value is between about 0.1 and 1.25, and wherein the cycle adjustment factor is between about -2 and 2. receiving a data set for a plurality of biological samples for a PCR amplification reaction, wherein the data set includes a plurality of amplification curves, each amplification curve associated with a biological sample of the plurality of biological samples; performing a constrained nonlinear optimization comprising a fit of each of the plurality of amplification curves to a modeled amplification curve to determine a best-fit set of parameters for a modeled efficiency curve and the modeled amplification curve, and wherein the best-fit set of parameters are used to create the modeled efficiency curve and the modeled amplification curve for each of the plurality of amplification curves; and determining a relative cycle threshold value, C RT, for each biological sample by using the modeled efficiency curve and the modeled amplification curve, wherein the constrained nonlinear optimization is a constrained non-linear parameter optimization, wherein the best-fit set of parameters for the modeled efficiency curve and the modeled amplification curve comprises three parameters being a curve shift parameter, a curve bend parameter, and a curve shift adjustment parameter, and comprises additionally two parameters being an amplification curve rising baseline slope parameter and an amplification curve relative amplification parameter for the modeled amplification curve, and said modeled efficiency curve is of a 3-parameter efficiency model using said three parameters and said modeled amplification curve is of a 5-parameter amplification model using said three parameters and said additionally two parameters, wherein using the modeled efficiency curve and the modeled amplification curve to determine the C RT value for each biological sample comprises: - using a selected efficiency value on the respective modeled efficiency curve to determine a reference threshold value on the respective modeled amplification curve; - multiplying the reference threshold value by a relative threshold fraction to determine a relative threshold fraction value on the respective modeled amplification curve to identify an unadjusted C RT; and - using a cycle adjustment factor to adjust the unadjusted C RT to obtain the C RT, - using a selected efficiency value on the respective modeled efficiency curve to determine a reference threshold value on the respective modeled amplification curve; - multiplying the reference threshold value by a relative threshold fraction to determine a relative threshold fraction value on the respective modeled amplification curve to identify an unadjusted C RT; and - using a cycle adjustment factor to adjust the unadjusted C RT to obtain the C RT, wherein determining the C RT is based on the efficiency value being selected from between about 0.15 to 0.5, and wherein the relative threshold fraction value is between about 0.1 and 1.25, and wherein the cycle adjustment factor is between about -2 and 2.