This paper is second in our series on deterministic modeling (DM) of infectious diseases. The first paper dealt with theories and methods of DM. The current paper provides sensitivity analyses. We used the SEIR model to show how changes in the transition rate from susceptibles to infectious (force of infection), variations in the latent and infectiousness period, and alteration to the vaccination proportion can alter the profile of common childhood epidemics. Various situations are explored so that the reader may grasp the effects of interventions, i.e., altering the main model parameters, upon the size and shape of epidemics, waiting times to epidemics, spreading out of infected cases in time, and switching from an epidemic to an endemic state and to cases eradication. The paper further shows that the introduction of infectious individuals into a community of susceptibles does not automatically give rise to an epidemic outbreak. This analysis thus provides the reader with an understanding of how epidemics evolve and how they can be controlled. Vaccination has been tackled as well as other public-health interventions that may have a bearing on the rate-limiting steps of epidemics. In spite of its limitations, the SEIR model helps gain insight into the dynamics of infectious diseases. Introduction This paper is an application of the theory and methods of deterministic modeling (DM) to common childhood diseases. It is the second in a series of three. The first paper (1) dealt with the theory and the methods of DM. In this paper, we will show how changes in the transition rates from susceptibles to infectious, or simply varying the other parameters of the SEIR deterministic model, can alter the profile of an epidemic. More specifically, we will look into the variations of the reproduction number, the duration of the latent period, and that of the period of infectiousness. A few situations will be explored in order to allow the reader to grasp the effects of change in these crucial epidemic parameters on the population pattern of infections. Our main disease reference will be measles, but varying the main infection parameters will cover a slew of other childhood diseases such as chicken-pox, mumps or rubella. Mainly, this paper will provide an overview of the potential of DM for the study of common childhood infections. Our aim is to provide the reader with useful insights into the mechanic and control of epidemics. A Model For Measles The first step in DM consists in having a complete and realistic picture of the biology of the study disease (e.g., period of infectivity, latent period, immune status after infection), and to select a parsimonious model (in relation to data available). In the case of measles, susceptibles get the virus and then become exposed (infected but not infectious) cases. After a given latent period, exposeds become infectious (and can infect newly susceptibles) until they recover. Measles provides long-lasting immunity after infection so that immunizeds (recovereds) do not become susceptibles anew. An appropriate continuous-time interval model for measles would be the SEIR model (Figure 1):
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