Tilahun Getachew Teshome, Makinde Oluwole Daniel, Malonza David
Pan African University Institute of Basic Sciences Technology and Innovation, Nairobi, Kenya.
Faculty of Military Science, Stellenbosch University, Stellenbosch, South Africa.
Comput Math Methods Med. 2017;2017:2324518. doi: 10.1155/2017/2324518. Epub 2017 Sep 10.
We propose and analyze a compartmental nonlinear deterministic mathematical model for the typhoid fever outbreak and optimal control strategies in a community with varying population. The model is studied qualitatively using stability theory of differential equations and the basic reproductive number that represents the epidemic indicator is obtained from the largest eigenvalue of the next-generation matrix. Both local and global asymptotic stability conditions for disease-free and endemic equilibria are determined. The model exhibits a forward transcritical bifurcation and the sensitivity analysis is performed. The optimal control problem is designed by applying Pontryagin maximum principle with three control strategies, namely, the prevention strategy through sanitation, proper hygiene, and vaccination; the treatment strategy through application of appropriate medicine; and the screening of the carriers. The cost functional accounts for the cost involved in prevention, screening, and treatment together with the total number of the infected persons averted. Numerical results for the typhoid outbreak dynamics and its optimal control revealed that a combination of prevention and treatment is the best cost-effective strategy to eradicate the disease.
我们提出并分析了一个用于伤寒热爆发以及在人口变化的社区中的最优控制策略的房室非线性确定性数学模型。使用微分方程稳定性理论对该模型进行定性研究，并从下一代矩阵的最大特征值获得代表流行指标的基本再生数。确定了无病平衡点和地方病平衡点的局部和全局渐近稳定性条件。该模型呈现出正向跨临界分岔并进行了敏感性分析。通过应用庞特里亚金极大值原理设计最优控制问题，采用三种控制策略，即通过环境卫生、适当卫生和疫苗接种进行预防策略；通过应用适当药物进行治疗策略；以及对携带者进行筛查。成本泛函考虑了预防、筛查和治疗所涉及的成本以及避免的感染人数总数。伤寒热爆发动态及其最优控制的数值结果表明，预防和治疗相结合是根除该疾病的最佳成本效益策略。
