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This study analyzes a mathematical model of two-strain infectious diseases where immunity wanes over time, such as influenza or dengue. The researchers used perturbation methods to determine when two disease strains can coexist in a population, finding that coexistence occurs either through convergence to a stable equilibrium or through sustained oscillations depending on specific parameter conditions. They identified two distinct parameter regimes with different qualitative behaviors and characterized the boundary between them.
Why it matters
Understanding multi-strain disease dynamics is crucial for predicting disease patterns and developing effective public health interventions for diseases with multiple circulating strains. The mathematical framework could help inform vaccination strategies and epidemic preparedness by clarifying conditions under which multiple strains persist versus when one strain dominates.
⚠️ Preprint – Noch nicht peer-reviewed
Dieser Artikel wurde noch nicht von unabhängigen Experten begutachtet. Die Ergebnisse sind vorläufig und sollten mit Vorsicht interpretiert werden.
Abstract: Many infectious diseases are comprised of multiple strains with examples including Influenza, tuberculosis, and Dengue virus. The time evolution of such systems is linked to a complex landscape shaped by interactions between competing strains. Possible long-term dynamics include the extinction of less competitive strains, convergence to multi-strain steady-states, or self-sustained oscillations. This work considers a two-strain epidemic model in which the strains can interact indirectly via the immunity response generated following infections, and in which this immune response wanes with time. In particular, we focus on scenarios where the rate of waning immunity is significantly faster than the rate of demographic turnover. The first key result of this study is the explicit computation of the steady states of the nonlinear system of seven equations. Following this result, we take advantage of the separation of time scales in the problem and use perturbation methods to analyze the stability of the fixed points. In particular, we establish the conditions under which the system gives rise to the coexistence of the two strains and whether coexistence is attained via convergence to an endemic steady-state or via self-sustained oscillations. Our study unveils two parameter regimes of distinct qualitative behavior of the system and characterizes the separatrix between them. Within the first regime, the system gives rise to oscillatory coexistence for all feasible conditions. In the second regime, the system’s behavior is governed by a solution to a quadratic equation, potentially resulting in the convergence to a multi-strain endemic equilibrium or the persistence of oscillatory coexistence.
Source: Dynamics of a two-strain epidemic model with waning immunity — a perturbative approach