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When Mathematics and Medicine Unite - A Review of the Use of Deterministic Compartmental Models in Epidemiology

DOI: 
10.7727/wimj.2017.113

ABSTRACT

Though Mathematics and Medicine at first glance appear to be disparate fields, their synergy is the basis of the field of infectious disease epidemiology and public health. Mathematical models have been used to guide policy decisions for the control of infectious diseases - most recently in the Ebola outbreak. Mathematical models can be used to generate estimates where data is sparse, examine possible “what if” scenarios and allow for the evaluation of control programs such as vaccination and quarantine. Modeling may also be used to explore the relative merits of different mitigation strategies both in preparation for and during an outbreak. One of the most useful concepts derived from these models is that of the basic reproduction number R0 which represents the number of new infections created by an infected individual introduced into a totally susceptible population. If R0 is less than 1 the disease disappears from the population but R0 greater than 1 indicates an epidemic. R0 varies for the same disease between different populations. R0 may be related to parameters such as the contact rate β which may vary in different scenarios such as isolation or use of vaccines.  Changes in the values of the contact rate may affect the value of R0 and a relatively small change in β near R0 = 1 may lead to the eradication of the disease. This ‘tipping point’ is called the bifurcation point  . Thus knowledge of β and its proximity to  enhances our predictive capability about the disease process under study. We caution however that model results should not be taken as predictions, but interpreted as theoretical projections based on assumptions and simplifications inherent in the model design.  

Accepted: 
13 Nov, 2017
e-Published: 15 Nov, 2017

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