A partial Lagrangian approach to mathematical models of epidemiology.

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dc.contributor.author Naz, R.
dc.contributor.author Naeem, I
dc.contributor.author Mahomed, F.M.
dc.date.accessioned 2016-06-06T14:00:49Z
dc.date.available 2016-06-06T14:00:49Z
dc.date.issued 2015
dc.identifier.citation Naz, R., Naeem, I.,and Mahomed, F.M. 2015. A partial Lagrangian approach to mathematical models of epidemiology. Mathematical Problems in Engineering en_ZA
dc.identifier.issn 1024-123X (Print)
dc.identifier.issn 1563-5147 (Online)
dc.identifier.uri http://hdl.handle.net/10539/20428
dc.description.abstract This paper analyzes the first integrals and exact solutions of mathematical models of epidemiology via the partial Lagrangian approach by replacing the three first-order nonlinear ordinary differential equations by an equivalent system containing one second order equation and a first-order equation. The partial Lagrangian approach is then utilized for the second-order ODE to construct the first integrals of the underlying system.We investigate the SIR and HIV models.We obtain two first integrals for the SIR model with and without demographic growth. For the HIV model without demography, five first integrals are established and two first integrals are deduced for the HIV model with demography. Then we utilize the derived first integrals to construct exact solutions to the models under investigation. The dynamic properties of these models are studied too. Numerical solutions are derived for SIR models by finite difference method and are compared with exact solutions. en_ZA
dc.language.iso en en_ZA
dc.publisher Hindawi Publishing Corporation en_ZA
dc.subject Diseases en_ZA
dc.subject Finite difference method en_ZA
dc.subject Nonlinear equations en_ZA
dc.subject Numerical methods en_ZA
dc.subject Ordinary differential equations en_ZA
dc.subject Differential equations en_ZA
dc.subject Population dynamics en_ZA
dc.subject Population statistics en_ZA
dc.title A partial Lagrangian approach to mathematical models of epidemiology. en_ZA
dc.type Article en_ZA


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