"This study provides a modified Bass model to deal with trend curves for basic issues of relevance to individuals from all over the world, for which we collected 16 data sets from 2004 to 2022 and that are available on Google servers as "google trends". It was discovered that the Bass model did not forecast well for curves that have a mono peak with a sharp decrease to some level then have semi-stable with small decrement sales for a long time, thus a new parameter based on r1 and r2 (ratios of average sales) was introduced, which improved the model's prediction ability and provided better results. The model was also applied to a data set taken from the Kaggle website about a subscriber digital product offering for financial services that include newsletters, webinars, and investment recommendations. The data contain 508932 data points about the products sold during 2016-2022. Compared to the traditional Bass model, the modified model showed better results in dealing with this condition, as the expected curve shape was closer to real sales, and the sum of squares error (SSE) value was reduced to a ratio ranging between (36.35-79.3%). Therefore, the improved model can be relied upon in these conditions."

翻译：本研究提出了一种改进的Bass模型，用于处理与全球个体相关的基础问题趋势曲线。为此，我们收集了2004年至2022年间的16组数据集，这些数据可从Google服务器以"谷歌趋势"形式获取。研究发现，对于呈现单峰形态、在剧烈下降至某水平后长期保持小幅递减半稳定状态的曲线，传统Bass模型的预测效果不佳。因此，本文引入了基于r1和r2（销售均值比率）的新参数，该改进显著提升了模型的预测能力并获得了更优结果。该模型还应用于从Kaggle网站获取的订阅型数字金融产品数据集（包含新闻通讯、网络研讨会及投资建议），该数据集包含2016-2022年间销售的508932个数据点。与传统Bass模型相比，改进模型在处理此类条件时表现出更优性能：其预期曲线形态更接近实际销售数据，且残差平方和（SSE）值降低幅度达36.35%-79.3%。因此，该改进模型可在此类条件下作为可靠预测工具。