Dynamics of malaria-dengue fever and its optimal control

Nita H. Shah; Ankush H. Suthar; Ekta N. Jayswal

doi:10.11121/ijocta.01.2020.00828

Authors

Nita H. Shah Department of Mathematics, Gujarat University, Ahmedabad-380009 http://orcid.org/0000-0003-1605-4778
Ankush H. Suthar Department of Mathematics, Gujarat University, Ahmedabad-380009 http://orcid.org/0000-0001-7583-450X
Ekta N. Jayswal Department of Mathematics, Gujarat University, Ahmedabad-380009 http://orcid.org/0000-0002-5888-2478

DOI:

https://doi.org/10.11121/ijocta.01.2020.00828

Keywords:

Malaria-dengue model, Basic reproduction number, Stability, Optimal control, Numerical Simulation

Abstract

The mosquito-borne infectious diseases like malaria and dengue are putative as important tropical infections and cause high morbidity and mortality around the world. In some cases, simultaneous coexistence of both the infections in one individual is seen which is very hard to distinguish as both diseases have almost similar symptoms. In this proposed article, dynamical system of non-linear differential equations is constructed with the help of mathematical modeling, which describe dynamics of the spread of these infectious diseases separately and concurrently. Basic reproduction number is evaluated to understand dynamical behaviour of the model. Local and global stability criteria have been deliberated rigorously. Control parameters are used to perceive effect of medication on these prevalent tropical diseases. Numerical simulations are used to observe effect of control parameters graphically.

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Author Biographies

Nita H. Shah, Department of Mathematics, Gujarat University, Ahmedabad-380009

Nita H. Shah is a Professor in the Department of Mathematics, Gujarat University, Ahmedabad. She has 25 years of research experience in inventory management, forecasting and information technology and information systems. She has published 375+ articles in international journals, including APJOR (Singapore), International Journal of Production Economics, OMEGA, CCERO (Belgium), ECPE (Romania), Measuring, Control & Simulation (France), JIOS (India), IJOMS (India), Industrial Engineering (India), European Journal of Operational Research, IJIR, IJOR, IJMOR, IJBPSCM, etc.

Ankush H. Suthar, Department of Mathematics, Gujarat University, Ahmedabad-380009

Ankush H. Suthar is research scholar in Department of Mathematics, Gujarat University, India. He is working in dynamical systems and mathematical modeling of health problem related to infectious diseases. He has published 2-papers in JMCS and IJCER on transmission of deadly infectious diseases like Nipah-virus and swine-flu.

Ekta N. Jayswal, Department of Mathematics, Gujarat University, Ahmedabad-380009

Ekta N. Jayswal is research scholar in Department of Mathematics, Gujarat University, India. She is working in finite dimensional dynamical systems and its stability. Her research interest is applications of mathematical modeling to resolve different environmental issues

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