Research Article

Health-worker emigration and the loss of disease control: a coupled workforce-epidemic model with burnout-driven attrition

Timothy Ado Shamaki1*
1 Federal University of Technology Babura
* Corresponding author: tashamaki.math@futb.edu.ng
Published: Oct, 2026
DOI: 10.68839/jpstma.2026.fvx2abgs
Pages: 27-46
Views: 52
Downloads: 24

Abstract

Nigeria has lost a large share of its health workforce to emigration, and surveys of Nigerian health workers link the wish to emigrate with burnout. This paper couples a treatable infection of SIS type to a health workforce that is trained, practises and emigrates. Treatment capacity is proportional to the practising workforce, and the emigration rate of practising workers rises with disease prevalence, which stands for workload. The analysis gives four main results. First, the basic reproduction number depends on the workforce only through its disease-free level, which yields explicit critical values of the workforce, the baseline emigration rate and the training intake. Second, burnout-driven emigration alone can make the bifurcation at the threshold backward, even when treatment does not saturate; an explicit index decides the direction, and centre manifold theory confirms it. Third, without treatment saturation the fold point, the width of the hysteresis interval and the jump in prevalence are given in closed form, and each agrees with an independent numerical computation to at least ten significant digits. Fourth, when saturation is moderate, every solution converges to an equilibrium. Numerical continuation shows that once control is lost, reducing emigration back to the critical rate does not restore it. A global sensitivity analysis shows that burnout leaves the reproduction number unchanged but raises the long-run prevalence after a large outbreak. Allowing emigrants to return lowers both the reproduction number and the index. The parameter values are illustrative assumptions, not estimates for Nigeria, so the numerical thresholds show what the model can do rather than where any real health system stands.

Keywords

Health-worker emigration; burnout; treatment capacity; backward bifurcation; hysteresis; global stability

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How to Cite

Shamaki, T. A. (2026). Health-worker emigration and the loss of disease control: a coupled workforce-epidemic model with burnout-driven attrition. Journal of Physical Sciences: Theories, Methods and Applications, 1(1), 27-46. https://doi.org/10.68839/jpstma.2026.fvx2abgs

T. A. Shamaki, "Health-worker emigration and the loss of disease control: a coupled workforce-epidemic model with burnout-driven attrition," Journal of Physical Sciences: Theories, Methods and Applications, vol. 1, no. 1, pp. 27-46, October 2026. doi: 10.68839/jpstma.2026.fvx2abgs

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