Perturbation and bifurcation analysis of a primary-secondary dengue infection transmission model with explicit vector dynamics and optimal control

Authors

  • Aloysius N. Ezaka
    Department of Mathematics/Statistics, Alex Ekwueme Federal University Ndufu Alike, Ebonyi State, Nigeria
  • Henry O. Adagba
    Department of Industrial Mathematics and Applied Statistics, Ebonyi State University, Abakaliki, Ebonyi State, Nigeria
  • Sunday N. Aloke
    Department of Industrial Mathematics and Health Statistics, David Umahi Federal University of Health Sciences, Uburu, Ebonyi State, Nigeria
  • Louis O. Omenyi
    Department of Mathematics/Statistics, Alex Ekwueme Federal University Ndufu Alike, Ebonyi State, Nigeria
  • Theresa E. Efor
    Department of Industrial Mathematics and Applied Statistics, Ebonyi State University, Abakaliki, Ebonyi State, Nigeria
  • Okorie Nwite
    Department of Industrial Mathematics and Applied Statistics, Ebonyi State University, Abakaliki, Ebonyi State, Nigeria
  • Chika Agha
    Department of Industrial Mathematics and Applied Statistics, Ebonyi State University, Abakaliki, Ebonyi State, Nigeria

Keywords:

Dengue, bifurcation, Perturbation, Reproduction number, Sensitivity

Abstract

A robust mathematical model of multi-strain dengue infection with explicit vector dynamics is formulated to incorporate optimal control and vaccination. The bifurcation coefficients were calculated, and their numerical perturbation led to transcritical, subcritical, and supercritical bifurcations. The results showed that the effective reproduction number of the model with control is sufficiently small compared with the basic reproduction number without control. The rate of secondary infection with control, ϕc, was also lower than the rate of secondary infection without control, ϕ0; that is, ϕc < ϕ0. The sensitivity results showed that the mosquito-to-human and human-to-mosquito interaction rates should be targeted by control interventions to reduce infection in the population.

Dimensions

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FIG 12

Published

2026-06-08

How to Cite

Perturbation and bifurcation analysis of a primary-secondary dengue infection transmission model with explicit vector dynamics and optimal control. (2026). African Scientific Reports, 5(2), 438. https://doi.org/10.46481/asr.2026.5.2.438

Issue

Volume 5, Issue 2, August 2026

Section

MATHEMATICAL SCIENCE SECTION
Copyright & Licensing

Copyright (c) 2026 Aloysius N. Ezaka, Henry O. Adagba, Sunday N. Aloke, Louis O. Omenyi, Theresa E. Efor, Okorie Nwite, Chika Agha

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Perturbation and bifurcation analysis of a primary-secondary dengue infection transmission model with explicit vector dynamics and optimal control. (2026). African Scientific Reports, 5(2), 438. https://doi.org/10.46481/asr.2026.5.2.438

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