Department of Mathematics, Natural and Computational Sciences, Debre Berhan University, Debre Birhan, Ethiopia.
Department of Mathematics, Natural and Computational Sciences, Oda Bultum University, Chiro, Ethiopia.
PLoS One. 2024 Oct 14;19(10):e0309356. doi: 10.1371/journal.pone.0309356. eCollection 2024.
A mathematical model of the dual addiction dissemination dynamics of alcoholism and smoking was created and examined in this work, along with cost-effectiveness and optimal control techniques. The primary goal of the research is to determine which cost-efficient management techniques are most helpful in lowering the problem of dual addiction dispersion in the community. The smoking addiction sub-model, the alcohol addiction sub-model, and the dual addiction model between alcohol and smoking were all calculated, and their stability was examined in this study. The effective reproduction numbers of the models are computed using the next-generation operator technique. When the model's effective reproduction number is smaller than one, the backward bifurcation phenomenon is seen. Six time-dependent control measures are taken into consideration when formulating and analyzing the optimum control issue. Utilizing and applying the parameter values and using MATLAB ode45 solver we performed numerical simulations for both the dual addiction model and its optimal control problem. Furthermore, using the incremental cost-effectiveness ratio (ICER), we carried out the cost-effectiveness analyses. The cost-effectiveness analysis shows that implementing all the protection (education) control measures simultaneously (i.e., implementing Strategy A) is the most cost-effective strategy. Finally, we recommend that the public health stakeholders must put great effort into the implementation of Strategy A to reduce the smoking and alcoholism dual addiction dissemination problem in the community.
本研究建立并探讨了一个酒精成瘾和吸烟双重成瘾传播动力学的数学模型，以及成本效益和最优控制技术。研究的主要目的是确定哪些具有成本效益的管理技术最有助于降低社区双重成瘾传播的问题。在本研究中，计算了吸烟成瘾子模型、酒精成瘾子模型以及酒精和吸烟之间的双重成瘾模型，并检验了它们的稳定性。使用下一代算子技术计算了模型的有效繁殖数。当模型的有效繁殖数小于 1 时，会出现后分叉现象。在制定和分析最优控制问题时，考虑了六种时变控制措施。我们使用 MATLAB ode45 求解器对双重成瘾模型及其最优控制问题进行了数值模拟。此外，我们还使用增量成本效益比（ICER）进行了成本效益分析。成本效益分析表明，同时实施所有保护（教育）控制措施（即实施策略 A）是最具成本效益的策略。最后，我们建议公共卫生利益相关者必须大力实施策略 A，以减少社区中吸烟和酒精成瘾的双重传播问题。
