A Partial Lagrangian Approach to Mathematical Models of Epidemiology

Abstract EN

This paper analyzes the first integrals and exact solutions ofmathematical models of epidemiology via the partial Lagrangianapproach by replacing the three first-order nonlinear ordinarydifferential equations by an equivalent system containing onesecond-order equation and a first-order equation.

The partialLagrangian approach is then utilized for the second-order ODE toconstruct the first integrals of the underlying system.

Weinvestigate the SIR and HIV models.

We obtain two first integralsfor the SIR model with and without demographic growth.

For the HIVmodel without demography, five first integrals are established andtwo first integrals are deduced for the HIV model with demography.

Then we utilize the derived first integrals to construct exactsolutions to the models under investigation.

The dynamic propertiesof these models are studied too.

Numerical solutions are derivedfor SIR models by finite difference method and are compared withexact solutions.