Dynamics of the optimality control of transmission of infectious disease: a sensitivity analysis

Over the course of history global population has witnessed deterioration of unprecedented scale caused by infectious transmission. The necessity to mitigate the infectious flow requires the launch of a well-directed and inclusive set of efforts. Motivated by the urge for continuous improvement in existing schemes, this article aims at the encapsulation of the dynamics of the spread of infectious diseases. The objectives are served by the launch of the infectious disease model. Moreover, an optimal control strategy is introduced to ensure the incorporation of the most feasible health interventions to reduce the number of infected individuals. The outcomes of the research are facilitated by stratifying the population into five compartments that are susceptible class, acute infected class, chronic infected class, recovered class, and vaccinated class. The optimal control strategy is formulated by incorporating specific control variables namely, awareness about medication, isolation, ventilation, vaccination rates, and quarantine level. The developed model is validated by proving the pivotal delicacies such as positivity, invariant region, reproduction number, stability, and sensitivity analysis. The legitimacy of the proposed model is delineated through the detailed sensitivity analysis along with the documentation of local and global features in a comprehensive manner. The maximum sensitivity index parameters are disease transmission and people moved from acute stages into chronic stages whose value is (0.439, 1) increase in parameter by 10 percent would increase the threshold quantity by (4.39, 1). Under the condition of a stable system, we witnessed an inverse relationship between susceptible class and time. Moreover, to assist the gain of the fundamental aim of this research, we take the control variables as time-dependent and obtain the optimal control strategy to minimize infected populations and to maximize the recovered population, simultaneously. The objectives are attained by the employment of the Pontryagin maximum principle. Furthermore, the efficacy of the usual health interventions such as quarantine, face mask usage, and hand sanitation are also noticed. The effectiveness of the suggested control plan is explained by using numerical evaluation. The advantages of the new strategy are highlighted in the article.