Modeling secondary infections with temporary immunity and disease enhancement factor: Mechanisms for complex dynamics in simple epidemiological models. (November 2022)

• Record Type: Journal Article
• Authors: Steindorf, Vanessa; Srivastav, Akhil Kumar; Stollenwerk, Nico; Kooi, Bob W.; Aguiar, Maíra
• Is Part Of: Chaos, solitons and fractals. Volume 164(2022)
• Publication Date: 2022-11
• Subjects: Bifurcation analysis -- Bi-stability -- Chaos -- Temporary immunity -- Disease enhancement -- Secondary infection; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2022.112709
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: Modeling insights for epidemiological scenarios characterized by chaotic dynamics have been largely unexplored. A rigorous analysis of such systems are essential for a real predictive power and a more accurate disease control decision making. Motivated by dengue fever epidemiology, we study a basic SIR–SIR type model for the host population, capturing differences between primary and secondary infections. This model is the minimalistic version to previously suggested multi-strain models for dengue fever in which deterministic chaos was found in wider parameter regions. Without strain structure of pathogens, we consider temporary immunity after a primary infection and disease enhancement in a subsequent infection to identify to which extent these biological mechanisms can generate complex behavior in simple epidemiological models. Stability analysis of the system is performed using the classical linearization theory, and the qualitative behavior of the model is investigated with a detailed bifurcation analysis. Rich dynamical structures are identified, including the Bogdanov–Takens, cusp and Bautin bifurcations which has never been described in dengue fever epidemiology. Besides the conventional transcritical bifurcation, a backward bifurcation occurs for higher disease enhancement in secondary infections, exhibiting bi-stability when biological temporary immunity period is assumed. The backward bifurcation is formalized using the center manifold theory. While the Hopf and the global homoclinic bifurcation curves were computed numerically, analytical expressions for the transcritical and tangent bifurcations are obtained. The combination of temporary immunity and disease enhancement play a significant role in the complexity of the system dynamics, with chaotic behavior observed after including seasonal forcing. Highlights: Biological features incorporated into simple epidemic models lead to rich dynamical behavior. Temporary immunity and disease enhancement play a major role in the dynamical system complexity. Backward bifurcation is found when enhancement factor ϕ > ϕ c > 1 . Bogdanov–Takens, cusp and Bautin bifurcations are described for the first time in dengue models. Chaotic behavior is observed after including seasonal forcing.