Olaniyi Samson, Chuma Furaha M, Lebelo Ramoshweu S, Ogbonna Richard C, Abimbade Sulaimon F
Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Ogbomoso, Nigeria.
Department of Physics, Mathematics and Informatics, Dar es Salaam University College of Education, Dar es Salaam, Tanzania.
PLoS One. 2025 Jan 30;20(1):e0318080. doi: 10.1371/journal.pone.0318080. eCollection 2025.
In this study, a new deterministic mathematical model based on fractional-order derivative operator that describes the pseudo-recovery dynamics of an epidemiological process is developed. Fractional-order derivative of Caputo type is used to examine the effect of memory in the spread process of infectious diseases with pseudo-recovery. The well-posedness of the model is qualitatively investigated through Banach fixed point theory technique. The spread of the disease in the population is measured by analysing the basic reproduction of the model with respect to its parameters through the sensitivity analysis. Consequently, the analysis is extended to the fractional optimal control model where time-dependent preventive strategy and treatment measure are characterized by Pontryagin's maximum principle. The resulting Caputo fractional-order optimality system is simulated to understand how both preventive and treatment controls affect the pseudo-recovery dynamics of infectious diseases in the presence of memory. Graphical illustrations are shown to corroborate the qualitative results, and to demonstrate the importance of memory effects in infectious disease modelling. It is shown that time-dependent preventive strategy and treatment measure in the presence of memory engenders significant reduction in the spread of the disease when compared with memoryless situation.
在本研究中，基于分数阶导数算子开发了一种新的确定性数学模型，该模型描述了一个流行病学过程的伪恢复动态。采用Caputo型分数阶导数来研究记忆在具有伪恢复的传染病传播过程中的作用。通过巴拿赫不动点理论技术对模型的适定性进行了定性研究。通过敏感性分析，分析模型的基本再生数相对于其参数的情况，以此衡量疾病在人群中的传播情况。因此，分析扩展到分数阶最优控制模型，其中时间依赖的预防策略和治疗措施由庞特里亚金极大值原理来刻画。对所得的Caputo分数阶最优性系统进行模拟，以了解在存在记忆的情况下，预防和治疗控制如何影响传染病的伪恢复动态。给出了图形说明，以证实定性结果，并证明记忆效应在传染病建模中的重要性。结果表明，与无记忆情况相比，存在记忆时的时间依赖预防策略和治疗措施能显著降低疾病的传播。
