Host contact structure is important for the recurrence of Influenza A

Abstract

An important characteristic of influenza A is its ability to escape host immunity through antigenic drift. A novel influenza A strain that causes a pandemic confers full immunity to infected individuals. Yet when the pandemic strain drifts, these individuals will have decreased immunity to drifted strains in the following seasonal epidemics. We compute the required decrease in immunity so that a recurrence is possible. Models for influenza A must make assumptions on the contact structure on which the disease spreads. By considering local stability of the disease free equilibrium via computation of the reproduction number, we show that the classical random mixing assumption predicts an unrealistically large decrease of immunity before a recurrence is possible. We improve over the classical random mixing assumption by incorporating a contact network structure. A complication of contact networks is correlations induced by the initial pandemic. We provide a novel analytic derivation of such correlations and show that contact networks may require a dramatically smaller loss of immunity before recurrence. Hence, the key new insight in our paper is that on contact networks the establishment of a new strain is possible for much higher immunity levels of previously infected individuals than predicted by the commonly used random mixing assumption. This suggests that stable contacts like classmates, coworkers and family members are a crucial path for the spread of influenza in human populations.

Epidemic dynamics of influenza-like diseases spreading in complex networks

“…Based on the classical susceptible-infectious-recovered (SIR) model, first formulated by Kermack and McKendrick [4], many scholars have extended it to investigate the spread and control of influenza (see, e.g., [5][6][7][8][9][10][11][12][13][14]). Before introducing the models in detail, we briefly describe two main epidemiological concepts involved in the infection of an individual [15].…”

“…The fraction of the susceptible, incubative, infectious, asymptomatic, and recovered individuals is denoted as S, L, I , A and R, respectively. As in equations (13) of Ref. [19], a five-dimensional system of the SLIAR model could be given by the following ordinary differential equations (ODEs):…”

“…Yuan et al [27] found that for slowly evolving contact networks, the basic reproduction number may attain its peak value when the population is still growing, in contrast to at equilibrium for classical homogeneous mixing epidemic models. Jaramillo et al [13] showed that by incorporating a contact network structure, the establishment of a new strain is possible for much higher immunity levels of previously infected individuals than that predicted by the homogeneous mixing assumption.…”