Mathematical and Stability Analysis of Dengue–Malaria Co-Infection with Disease Control Strategies

Azhar Iqbal Kashif Butt (), Muhammad Imran (), Brett A. McKinney, Saira Batool and Hassan Aftab
Additional contact information
Azhar Iqbal Kashif Butt: Department of Mathematics and Statistics, College of Science, King Faisal University, Al-Ahsa 31982, Saudi Arabia
Muhammad Imran: Tandy School of Computer Science, University of Tulsa, Tulsa, OK 74104, USA
Brett A. McKinney: Tandy School of Computer Science, University of Tulsa, Tulsa, OK 74104, USA
Saira Batool: Tandy School of Computer Science, University of Tulsa, Tulsa, OK 74104, USA
Hassan Aftab: Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan

Mathematics, 2023, vol. 11, issue 22, 1-28

Abstract: Historically, humans have been infected by mosquito-borne diseases, including dengue fever and malaria fever. There is an urgent need for comprehensive methods in the prevention, control, and awareness of the hazards posed by dengue and malaria fever to public health. We propose a new mathematical model for dengue and malaria co-infection with the aim of comprehending disease dynamics better and developing more efficient control strategies in light of the threat posed to public health by co-infection. The proposed mathematical model comprises four time-dependent vector population classes ( S E I d I m ) and seven host population classes ( S E I d I m I d m T R ). First, we show that the proposed model is well defined by proving that it is bounded and positive in a feasible region. We further identify the equilibrium states of the model, including disease-free and endemic equilibrium points, where we perform stability analysis at equilibrium points. Then, we determine the reproduction number R 0 to measure the level of disease containment. We perform a sensitivity analysis of the model’s parameters to identify the most critical ones for potential control strategies. We also prove that the proposed model is well posed. Finally, the article examines three distinct co-infection control measures, including spraying or killing vectors, taking precautions for one’s own safety, and reducing the infectious contact between the host and vector populations. The control analysis of the proposed model reveals that all control parameters are effective in disease control. However, self-precaution is the most effective and accessible method, and the reduction of the vector population through spraying is the second most effective strategy to implement. Disease eradication is attainable as the vector population decreases. The effectiveness of the implemented strategies is also illustrated with the help of graphs.

Keywords: mathematical model; dengue–malaria co-infection; stability analysis; sensitivity analysis; control analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/22/4600/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/22/4600/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:22:p:4600-:d:1277308

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().