Dynamics of a fractional COVID-19 model with immunity using harmonic incidence mean-type.

The transmission dynamics of COVID-19 is investigated through the prism of the Atangana-Baleanu fractional model with acquired immunity. Harmonic incidence mean-type aims to drive exposed and infected populations towards extinction in a finite time frame. The reproduction number is calculated based on the next-generation matrix. A disease-free equilibrium point can be achieved globally using the Castillo-Chavez approach. Using the additive compound matrix approach, the global stability of endemic equilibrium can be demonstrated. Utilizing Pontryagin's maximum principle, we introduce three control variables to obtain the optimal control strategies. Laplace transform allows simulating the fractional-order derivatives analytically. Analysis of the graphical results led to a better understanding of the transmission dynamics.

Optimal control for co-infection with COVID-19-Associated Pulmonary Aspergillosis in ICU patients with environmental contamination.

In this paper, we propose a mathematical model for COVID-19-Associated Pulmonary Aspergillosis (CAPA) co-infection, that enables the study of relationship between prevention and treatment. The next generation matrix is employed to find the reproduction number. We enhanced the co-infection model by incorporating time-dependent controls as interventions based on Pontryagin's maximum principle in obtaining the necessary conditions for optimal control. Finally, we perform numerical experiments with different control groups to assess the elimination of infection. In numerical results, transmission prevention control, treatment controls, and environmental disinfection control provide the best chance of preventing the spread of diseases more rapidly than any other combination of controls.