A Partial Lagrangian Approach to Mathematical Models of Epidemiology
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....
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2015-01-01
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| Series: | Mathematical Problems in Engineering |
| Online Access: | http://dx.doi.org/10.1155/2015/602915 |
| Summary: | 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. |
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| ISSN: | 1024-123X 1563-5147 |