PS01 MEPI-26

A Stage-Structured Discrete SIRS Modeling of Viral Transmission in Fish Populations

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Ghazale Farjam

Departments of Mathematics and Statistics, University of Manitoba
"A Stage-Structured Discrete SIRS Modeling of Viral Transmission in Fish Populations"
Climate change is profoundly transforming Arctic ecosystems, increasing the vulnerability of native fish populations to emerging viral pathogens. Conducting empirical research on aquatic species, particularly in remote Arctic regions, is often hindered by limited accessibility and data scarcity (Desforges et al., 2022). Modeling approaches are therefore essential tools for understanding disease dynamics and informing conservation strategies in these environments. Discrete-time models have been widely used in population biology (Elaydi & Cushing, 2025). To investigate the complex dynamics of disease transmission across life stages, we developed a discrete-time, stage-structured SIRS (Susceptible–Infected–Recovered–Susceptible) model that incorporates larval, juvenile, and adult life stages. This model is enhanced by the integration of survival terms to better capture life-cycle complexity and pathogen transmission. It includes key demographic and epidemiological processes such as age-specific mortality, aging, horizontal and vertical transmission, recovery, and waning immunity. Our main focus is on modeling the transmission of viral pathogens within and between four fish species (Dolly Varden, Arctic Charr, Sockeye Salmon, and Chum Salmon) across freshwater and marine environments in the western Canadian Arctic. To establish a foundational understanding of the system’s behavior, we initially consider a single-patch, single-population setting with a time-invariant transition matrix, enabling tractable analysis of disease dynamics (Caswell, 2001). This simplified framework facilitates analytical exploration of disease thresholds, the basic reproduction number R₀, and the long-term viability of infected fish populations. Parameterization of the model is guided by empirical studies on Arctic fish ecology and disease surveillance, ensuring biological realism (Niemi et al., 2024).


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Annual Meeting for the Society for Mathematical Biology, 2025.