In the present paper, we formulate a new mathematical model for the dynamics of moral corruption with comprehensive age-appropriate sexual information and provision of guidance and counselling. The population is subdivided into three (3) different compartments according to their level of information on sexual matters. The model is proved to be both epidemiologically and mathematically well posed. The existence of unique morally corrupt-free and endemic equilibrium points is investigated. The basic reproduction number with respect to morally corrupt-free equilibrium is obtained using next generation matrix approach to monitor the dynamics of corrupt morals and ascertain its level in order to suggest effective intervention strategies to control this problem. The local as well as global asymptotic stability of these equilibrium points is studied. The analysis reveals a globally asymptotically stable morally corrupt-free equilibrium whenever and a globally asymptotically stable endemic equilibrium if otherwise. Further analysis, using center manifold theory, shows that the model exhibits forward bifurcation insinuating that the classical epidemiological requirement of is necessary and sufficient for elimination of moral corruption. A brief discussion on the graphical results using the available numerical procedures is shown. From numerical simulations, it was ascertain that integrated control strategy is the best approach to fight against moral corruption transmission. Lastly, some key parameters that show significance in the moral corruption elimination from the society are also exploited.

中文翻译：

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肯尼亚青少年道德腐败和控制措施的数学建模与分析

在本文中，我们使用适合年龄的全面性信息以及提供指导和咨询，为道德腐败的动态发展建立了一个新的数学模型。根据他们关于性事务的信息水平，将其分为三（3）个不同的部分。该模型在流行病学和数学上都被证明是正确的。研究了独特的无道德腐败和地方性均衡点的存在。关于下一代道德无腐败均衡的基本再生产数是使用下一代矩阵方法来监测腐败道德的动态并确定其水平的，从而提出有效的干预策略来控制这一问题。研究了这些平衡点的局部和全局渐近稳定性。否则，则为全局渐近稳定的地方均衡。使用中心流形理论的进一步分析表明，该模型表现出前向分歧，这说明了经典的流行病学要求是消除道德腐败的必要条件和充分条件。显示了使用可用数值程序对图形结果的简短讨论。从数值模拟可以确定，综合控制策略是与道德腐败传播作斗争的最佳方法。最后，还利用了一些对消除社会道德腐败具有重要意义的关键参数。