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

Table 2

Dependence of antigenic diversity structure in the steady coexistence on the transmission rates. Other parameter values are immunity period = 3 years, transmission rate of single infections (𝛽₁)=1.0, and infectious period = 2 days; hence 𝑅₀=2.0 for single infection; ten indistinguishable strains (𝑛=10) are assumed to cocirculate while three models are considered in which the most complex coinfections are of multiplicity 𝑚=2,3,4 strains, respectively.

𝑚	𝛽2	𝛽3	𝛽4	𝜙	𝑝	𝑝1	𝑝2	𝑝3	𝑝4
4	0.5	0.0	0.0	0.75	9.535×10^−4	9.502×10^−4	3.263×10^−6	7.469×10^−9	1.664×10^−11
		0.4	0.0	0.75	9.535×10^−4	9.502×10^−4	3.274×10^−6	1.253×10^−8	3.019×10^−11
		0.4	0.4	0.75	9.535×10^−4	9.502×10^−4	3.274×10^−6	1.256×10^−8	5.038×10^−11
		0.4	0.4	0.0^$	9.487×10^−4	9.455×10^−4	3.214×10^−6	1.214×10^−8	4.826×10^−11
	0.75	0.0	0.0	0.38	9.535×10^−4	9.470×10^−4	6.444×10^−6	1.714×10^−8	6.170×10^−11
		0.6	0.0	0.38	9.536×10^−4	9.470×10^−4	6.529×10^−6	4.349×10^−8	1.328×10^−10
		0.6	0.4	0.38	9.536×10^−4	9.470×10^−4	6.534×10^−6	4.369×10^−8	2.218×10^−10
		0.6	0.4	0.0^$	9.487×10^−4	9.423×10^−4	6.386×10^−6	4.209×10^−8	2.117×10^−10
3	0.5	0.0	—	0.75	9.535×10^−4	9.502×10^−4	3.263×10^−6	7.478×10^−9	—
		0.4	—	0.75	9.535×10^−4	9.502×10^−4	3.274×10^−6	1.249×10^−8	—
		0.4	—	0.0^$	9.486×10^−4	9.454×10^−4	3.213×10^−6	1.216×10^−8	—
2	0.5	—	—	0.75	9.535×10^−4	9.502×10^−4	3.256×10^−6	—	—
		—	—	0.0^$	9.486×10^−4	9.454×10^−4	3.223×10^−6	—	—

$These coexistence equilibria are unstable.