First integrals and exact solutions of the SIRI and tuberculosis models |
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| Authors: | R Naz K S Mahomed I Naeem |
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| Institution: | 1. Centre for Mathematics and Statistical Sciences, Lahore School of Economics, Lahore, Pakistan;2. DST‐NRF Centre of Excellence in Mathematical and Statistical Sciences, School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, South Africa;3. Department of Mathematics, School of Science and Engineering,LUMS, Lahore, Pakistan |
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| Abstract: | The first integrals and exact solutions of mathematical models of epidemiology: a susceptible‐infected‐recovered‐infected (SIRI) model and a tuberculosis model with demographic growth are analyzed. These models are represented by systems of first‐order nonlinear ordinary differential equations, and this system is replaced by one which contains a second‐order ordinary differential equation. The partial Lagrangian approach is then utilized to derive the first integrals of these models. Several cases arise. Then, we utilize the derived first integrals to construct exact solutions for the models under investigation and determine new solutions. The dynamic properties of these models are studied too. Copyright © 2016 John Wiley & Sons, Ltd. |
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| Keywords: | symmetries Lie‐group and Lie– algebra methods methods of ordinary differential equations |
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