Understanding the transmission dynamics of respiratory syncytial virus using multiple time series and nested models

Abstract

The nature and role of re-infection and partial immunity are likely to be important determinants of the transmission dynamics of human respiratory syncytial virus (hRSV). We propose a single model structure that captures four possible host responses to infection and subsequent reinfection: partial susceptibility, altered infection duration, reduced infectiousness and temporary immunity (which might be partial). The magnitude of these responses is determined by four homotopy parameters, and by setting some of these parameters to extreme values we generate a set of eight nested, deterministic transmission models. In order to investigate hRSV transmission dynamics, we applied these models to incidence data from eight international locations. Seasonality is included as cyclic variation in transmission. Parameters associated with the natural history of the infection were assumed to be independent of geographic location, while others, such as those associated with seasonality, were assumed location specific. Models incorporating either of the two extreme assumptions for immunity (none or solid and lifelong) were unable to reproduce the observed dynamics. Model fits with either waning or partial immunity to disease or both were visually comparable. The best fitting structure was a lifelong partial immunity to both disease and infection. Observed patterns were reproduced by stochastic simulations using the parameter values estimated from the deterministic models.

Mathematical modelling of virus RSV: qualitative properties, numerical solutions and validation for the case of the region of Valencia.

“…Hence, it is reasonable to seek conditions under which two generalized models for transmission of seasonal diseases would have a positive periodic solution. Thus, we conjecture that the analytical solutions of the models presented in (Weber et al, 2001), White et al (2007), that model the behavior of the transmission of RSV , should be periodical. To do this, we use a Theorem of Continuation by Jean Mawhin, which, under conditions on the rate transmission β(t) and the others parameters of the model, ensures the existence of positive periodic solutions.…”

“…In modeling of transmission of seasonal diseases, nonlinear systems of ordinary differential equations have been used with a coefficient given by a periodic continuous functions β(t) (called sometimes seasonallyforced function) that incorporates the seasonality of the spread in the environment, see Diallo and Koné (2007), Anderson and May (1991), Keeling et al (2001), White et al (2005), White et al (2007), Weber et al (2001), Moneim and Greenhalgh (2005), Greenhalgh and Moneim (2003). Many authors take, as an example of seasonally-forced function, the expression β(t) = b 0 (1 + b 1 cos(2π(t + ϕ)), where b 0 > 0 is the baseline transmission parameter, 0 < b 1 ≤ 1 measures the amplitude of the seasonal variation in transmission and 0 ≤ ϕ ≤ 1 is the normalized phase angle.…”

“…A classical technique for modeling infectious diseases in the population is to use systems of ordinary differential equations, describing the evolution of the number of individuals in the different subpopulations. In this sense, mathematical models using system of nonlinear ordinary differential equations of the first order for RSV have been developed in Weber et al (2001), White et al (2005), White et al (2007), Arenas et al (2009c). These papers interpret the pattern of seasonal epidemics of RSV disease observed in different countries and estimate the epidemic and eradication thresholds for the RSV infection.…”

“…Modeling the spread of seasonal epidemiological diseases: theory and applications interruption of the infections chain during vacations or the inclusion of new individuals at the beginning of each school year (Dietz and Schenzle, 1985). Some models use a time-varying contact rate β(t) between susceptible and infected individuals called as seasonally-forced function (Diallo and Koné, 2007), (Anderson and May, 1991), (Keeling et al, 2001), (White et al, 2005), (White et al, 2007), (Weber et al, 2001), (Moneim and Greenhalgh, 2005), (Greenhalgh and Moneim, 2003). An example of seasonally-forced function is β(t) = b 0 (1 + b 1 cos(2π(t + ϕ))) where b 0 > 0 is the baseline transmission parameter, 0 < b 1 ≤ 1 measures the amplitude of the seasonal variation in transmission and 0 ≤ ϕ ≤ 1 is the phase angle normalized.…”

“…The transmission dynamics of RSV are strongly seasonal with a pronounced annual or biannual component in many countries. Epidemics occur each winter in many temperate climates and are often coincident with seasonal rainfall and religious festivals in tropical countries (White et al, 2007), (White et al, 2005).…”