Who Should be Controlled? The Role of Asymptomatic Individuals, Isolation and Switching in the Dominant Transmission Route in Classical and Network Epidemic Models.

We introduce two mathematical models for the spread of an SIR-type infectious disease, incorporating direct (person-to-person) and indirect (environment-to-person) transmissions, latent periods, asymptomatic infections, and different isolation rates for exposed, asymptomatic and symptomatic individuals. The first model employs the classical homogeneous mixing approach, while the second uses the edge-based compartmental approach to consider heterogeneity in the number of contacts within the population through a random contact network. Key epidemiological metrics, including the basic reproduction number and final epidemic size, are derived and illustrated through simulations for both models. Motivated by emerging infectious diseases with multiple transmission routes such as cholera and Mpox, we conduct sensitivity analyses to assess the impact of parameter variations and control measures. We also explore how secondary transmission routes influence disease spread and when the dominant route may switch over time. In this respect, our main theoretical results demonstrate that such a 'switching phenomenon' cannot occur in homogeneous mixing models or Poissonian networks when person-to-person transmission initially dominates, while numerical simulations show that it may occur in other networks such as scale-free and regular networks. These findings highlight the risks of designing public health interventions based solely on early disease dynamics and provide insights into controlling infections with multiple transmission routes.