Final answer:
The period of illness is the stage where a patient has the greatest risk of transmitting the infection to others, due to the high number of pathogens and severe symptoms.
Step-by-step explanation:
The stage of development of an infection during which a patient presents the greatest risk to others is the period of illness. This is the third stage of acute disease, where the number of pathogens is the highest and the signs and symptoms are most severe. During this period, the infectiousness of the disease is typically at its peak, and there is a high risk of transmitting the infection to other individuals.
For instance, diseases with rashes like chickenpox and measles can make a patient contagious even before the rash develops, within the incubation period. On the other hand, respiratory infections such as the common cold and influenza render the patient contagious from the onset of the prodromal period. Even in the periods of decline and convalescence, patients can still pose a risk of transmission depending on the disease and the pathogen involved.