Internet of Things (IoT) of networked robots installed at the edges of smart healthcare infrastructure (SHI) can be used to mitigate infectious diseases. Such robots can predict pandemics, and screen, diagnose, treat or perform healthcare nursing for infectious diseases. When equipped with suitable digital technologies, these robots can mitigate epidemics and predict future pandemics more efficiently. This paper proposes a co-infection model of infectious diseases, using HIV/AIDS and COVID-19 (or HAC-19) as examples, that can underlie SHI nodes (e.g., robots). The co-infection model benefits from the compartmental applications of fractional derivatives to healthcare problems. Six co-infection control parameters (e.g., awareness, counselling, COVID-19 safety protocol, COVID-19 vaccine, HIV/AIDS therapy, and COVID-19 treatment) are used to evaluate the effectiveness of the proposed model. The HAC-19 model uses a basic reproduction number to indicate the effectiveness of the control measures. When the control parameters are effective, the results show that the HAC-19 co-infection reduces to a minimum in the population. When the control measures are not effective, the HAC-19 co-infection will be endemic. Robots, equipped with IoT at the edge of the SHI, transfer the data from the trials to the outpost network nodes in the hospital and then to the cloud for further analytics and decision-making. The results of real-world trials at three hospital locations strongly agree with the theoretical model.