Modeling and Control of Epidemics

  • H. T. Banks
Part of the Lecture Notes in Biomathematics book series (LNBM, volume 6)


One of the early attempts at mathematical modeling of the dynamics involved in the spread of disease was reported in [157], The work of Sir Ronald Ross (1908–1911) on the spread of malaria is by now well known and, in fact, much of the practical work carried out later stemmed from Ross’ investigations. In deriving his model consisting of two nonlinear ordinary differential equations of the form
$$ \begin{array}{*{20}{c}} {\dot{x}\left( t \right) = ay\left( t \right)\left\{ {\frac{{b - x\left( t \right)}}{b}} \right\} - rx\left( t \right)} \hfill \\ {\dot{y}\left( t \right) = cx\left( t \right)\left\{ {\frac{{d - y\left( t \right)}}{d}} \right\} - ey\left( t \right),} \hfill \\ \end{array} $$
Ross ignored latency periods but subsequently pointed out that the model equations would become differential-difference equations if the latent periods were considered.


Corrective Action Epidemic Model Passive Immunization Nonlinear Ordinary Differential Equation Infectious Period 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • H. T. Banks
    • 1
  1. 1.Lefschetz Center for Dynamical Systems Division of Applied MathematicsBrown UniversityProvidenceUSA

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