The Impact of Coinfections and Their Simultaneous Transmission on Antigenic Diversity and Epidemic Cycling of Infectious Diseases

Figure 8

Impact of efficiency of single transmission (𝜙) and simultaneous transmissibility (𝑅^𝑑₀) from dual infection on the distribution of equilibria. The four equilibria on the (𝑅^𝑎₀,𝑅^𝑏₀) plane are separated by four curves: 𝑅^𝑎₀=1, 𝑅^𝑏₀=1, 𝑅^𝑏₀(𝑄^∗_𝑎)=1, and 𝑅^𝑎₀(𝑄^∗_𝑏)=1. In panel (a) where 𝑅^𝑑₀=0 and 𝜙≤0.5 or 𝑅^𝑑₀=𝑅^𝑎₀/2 and 𝜙≤0.25,  𝑅^𝑏₀>𝑅^𝑎₀ is required to maintain 𝑅^𝑏₀(𝑄^∗_𝑎)≥1 (and similarly requiring 𝑅^𝑎₀>𝑅^𝑏₀ to maintain 𝑅^𝑎₀(𝑄^∗_𝑏)≥1); hence no coexistence is possible. In panels (b) and (c) we consider the symmetric situation in which 𝜙_𝑎=𝜙_𝑏=𝜙=5 under different simultaneous transmissibility. The other parameters are infectious period (1/𝛾_𝑎=1/𝛾_𝑏=1/𝛾_𝑑)=2 days, immunity period = 3 years, and life span = 55 years.

(a) 𝑅^𝑑₀=0 and 𝜙≤0.5 or 𝑅^𝑑₀=𝑅^𝑎₀/2 and 𝜙≤0.25

(b) 𝑅^𝑑₀=0 and 𝜙=5

(c) 𝑅^𝑑₀=𝑅^𝑎₀/2 and 𝜙=5