Modeling COVID-19 pneumonia and COVID-associated pulmonary aspergillosis: sensitivity analysis and optimal control.

Severe cases of COVID-19 can progress to pneumonia and, in some patients, to COVID-19-associated pulmonary aspergillosis (CAPA), a fungal co-infection linked to high mortality. Most existing models address COVID-19 transmission alone, without explicitly capturing the sequential progression to pneumonia and CAPA. To address this gap, we develop a novel compartmental model (SII_cpI_caHR) that integrates the co-dynamics of COVID-19 pneumonia and CAPA, incorporating both disease progression pathways and hospitalisation processes. The model is calibrated using cumulative COVID-19 case data from India, and analysed through stability theory, sensitivity analysis, and an optimal control framework. Sensitivity indices and Partial Rank Correlation Coefficients identify key parameters influencing transmission and severity. We evaluate time-dependent intervention strategies-vaccination, early hospitalisation, and enhanced treatment-individually and in combination, using Pontryagin's Maximum Principle and numerical simulation. Results show that while each single measure reduces disease burden, combined application of all three significantly minimises pneumonia and CAPA prevalence, lowers hospitalisation needs, and is cost-effective within realistic constraints. These findings emphasise the importance of integrated public health strategies that couple pharmaceutical and clinical interventions to curb severe COVID-19 outcomes and associated fungal complications.