This paper proposes a compartmental model with multiple ideologies based on the mechanism of overlapping infections of contagious diseases to describe the individual radicalization of terrorism process under the influence of two cooperative ideologies. The two ideologies attract their respective supporters in the same sensitive group. The supporters of each ideology can be divided into sympathizers and defenders according to extreme levels. Cross-interaction between the two types of sympathizers is introduced. Through the interaction, sympathizers can be influenced by other ideologies and thus become more extreme. Use a set of differential equations to mathematically simulate the update process. The research results show that ideologies with cooperative mechanisms are easier to establish themselves in a group and are difficult to eliminate. This makes it more difficult to curb radicalization of the population. Based on the model, several strategies are assessed to counter radicalization.