When Reducing Transmission Is Not Enough: Carrier Dynamics and Backward Bifurcation in Influenza-Pneumococcal Co-infection
Abstract
Bacterial co-infection, particularly with \emph{Streptococcus pneumoniae}, is a major driver of morbidity during influenza epidemics, and this burden falls disproportionately on sub-Saharan Africa, where both pathogens circulate year-round at high levels and pneumococcal carriage remains common and persistent across the region. Yet existing mathematical models rarely track a host's bacterial carriage status jointly with their full influenza history through recovery. We develop a twelve-compartment ODE model that classifies each host by viral status (susceptible, infected, recovered) and bacterial status (susceptible, carrier, actively infected, recovered), allowing carrier-to-active progression to depend on prior influenza exposure. We establish positivity, boundedness, and a positively invariant region, then derive the basic reproduction number ℛ0 and quasi-endemic equilibria of a single disease, together with invasion reproduction numbers InvB and InvV quantifying each pathogen's ability to invade a population where the other is already endemic. Center-manifold analysis shows that the bacterial subsystem and the full coexistence equilibrium undergo a backward bifurcation precisely when carrier transmission exceeds the carrier's total exit rate, βc>κS+θ+μ, so that reducing ℛ0 below one is not sufficient for elimination, while the viral subsystem bifurcates forward. A global sensitivity analysis (Latin Hypercube Sampling with partial rank correlation coefficients) shows that the viral and bacterial thresholds are governed by largely separate parameters, while the bacterial invasion potential is strongly shaped by viral transmission and recovery, giving a quantitative signature of cross-pathogen synergy.
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BibTeX
@misc{fome2026when,
title = {{When Reducing Transmission Is Not Enough: Carrier Dynamics and Backward Bifurcation in Influenza-Pneumococcal Co-infection}},
author = {A. D. Fome and W. Bock and T. Goetz},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09978},
eprint = {2610.09978},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09978},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - When Reducing Transmission Is Not Enough: Carrier Dynamics and Backward Bifurcation in Influenza-Pneumococcal Co-infection
AU - A. D. Fome
AU - W. Bock
AU - T. Goetz
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.09978
UR - https://arxiv.org/abs/2610.09978
AB - Bacterial co-infection, particularly with \emph{Streptococcus pneumoniae}, is a major driver of morbidity during influenza epidemics, and this burden falls disproportionately on sub-Saharan Africa, where both pathogens circulate year-round at high levels and pneumococcal carriage remains common and persistent across the region. Yet existing mathematical models rarely track a host's bacterial carriage status jointly with their full influenza history through recovery. We develop a twelve-compartment ODE model that classifies each host by viral status (susceptible, infected, recovered) and bacterial status (susceptible, carrier, actively infected, recovered), allowing carrier-to-active progression to depend on prior influenza exposure. We establish positivity, boundedness, and a positively invariant region, then derive the basic reproduction number ℛ_0 and quasi-endemic equilibria of a single disease, together with invasion reproduction numbers Inv^B and Inv^V quantifying each pathogen's ability to invade a population where the other is already endemic. Center-manifold analysis shows that the bacterial subsystem and the full coexistence equilibrium undergo a backward bifurcation precisely when carrier transmission exceeds the carrier's total exit rate, β_c>κ_S+θ+μ, so that reducing ℛ_0 below one is not sufficient for elimination, while the viral subsystem bifurcates forward. A global sensitivity analysis (Latin Hypercube Sampling with partial rank correlation coefficients) shows that the viral and bacterial thresholds are governed by largely separate parameters, while the bacterial invasion potential is strongly shaped by viral transmission and recovery, giving a quantitative signature of cross-pathogen synergy.
ER -