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International Journal of Nonlinear Sciences and Numerical Simulation

Editor-in-Chief: Birnir, Björn

Editorial Board: Armbruster, Dieter / Chen, Xi / Bessaih, Hakima / Chou, Tom / Grauer, Rainer / Marzocchella, Antonio / Rangarajan, Govindan / Trivisa, Konstantina / Weikard, Rudi

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Volume 19, Issue 6

Issues

Stability, Bifurcation and Optimal Control Analysis of a Malaria Model in a Periodic Environment

Prabir Panja / Shyamal Kumar Mondal
  • Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore -721 102, W.B., India
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/ Joydev Chattopadhyay
Published Online: 2018-07-20 | DOI: https://doi.org/10.1515/ijnsns-2017-0221

Abstract

In this paper, a malaria disease transmission model has been developed. Here, the disease transmission rates from mosquito to human as well as human to mosquito and death rate of infected mosquito have been constituted by two variabilities: one is periodicity with respect to time and another is based on some control parameters. Also, total vector population is divided into two subpopulations such as susceptible mosquito and infected mosquito as well as the total human population is divided into three subpopulations such as susceptible human, infected human and recovered human. The biologically feasible equilibria and their stability properties have been discussed. Again, the existence condition of the disease has been illustrated theoretically and numerically. Hopf-bifurcation analysis has been done numerically for autonomous case of our proposed model with respect to some important parameters. At last, a optimal control problem is formulated and solved using Pontryagin’s principle. In numerical simulations, different possible combination of controls have been illustrated including the comparisons of their effectiveness.

Keywords: malaria; global stability; basic reproduction number; control parameters; Hopf bifurcation; optimal control

MSC 2010: 92B05; 37C60; 37C10

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About the article

Received: 2017-10-10

Accepted: 2018-05-20

Published Online: 2018-07-20

Published in Print: 2018-09-25


Citation Information: International Journal of Nonlinear Sciences and Numerical Simulation, Volume 19, Issue 6, Pages 627–642, ISSN (Online) 2191-0294, ISSN (Print) 1565-1339, DOI: https://doi.org/10.1515/ijnsns-2017-0221.

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