Formulations of antibody cross-reaction hypotheses in host-to-host transmission models.

<p> is the transmission rate, represents the number of individuals infected with serotype and the number of individuals subsequently infected with serotypes and .</p>*<p>In references <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0049085#pone.0049085-Aguiar1" target="_blank">[113]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0049085#pone.0049085-Aguiar2" target="_blank">[114]</a>, Aguiar <i>et al.</i> assumed that a proportion of secondary infected individuals contribute to a lesser extent to the epidemic process due to hospitalisation or isolation. This assumption is based on the evidence that secondary infections are more likely to produce severe clinical expression of the disease. As the antagonist relationship between previously acquired antibodies and secondary infection with an heterologous serotype is certainly involved in the intra-individual disease evolution, we classified this assumption as depending on the antibody cross-reaction hypotheses.