A mean field analysis of the role of indirect transmission in emergent infection events

Abstract: We developed a mathematical model to investigate the role of indirect transmission in the spread of infectious diseases, using the illustrative example of sarcoptic mange as a case study. This disease can be transmitted through direct contact between an infected host and a susceptible one, or indirectly when potential hosts encounter infectious mites and larvae deposited in the environment, commonly referred to as fomites. Our focus is on exploring the potential of these infectious reservoirs as triggers for emerging infection events and as stable reservoirs of the disease. To achieve this, our mean field compartmental model incorporates the epidemiological dynamics driven by indirect transmission via fomites. We identify different types of dynamics that the system can go into, controlled by different levels of direct and indirect transmission. Among these, we find a new regime where the disease can emerge and persist over time solely through fomites, without the necessity for direct transmission. This possibility of the system reveals an evolutionary pathway that could enable the parasite to enhance its fitness beyond host co-evolution. We also define a new threshold based on an effective reproductive number, that enables us to predict the conditions for disease persistence. Our model allows us to assess the potential effectiveness of various disease intervention measures by incorporating a feature observed in real systems. We hope this contributes to a better understanding of infectious disease outbreaks.