Modeling secondary infections with temporary immunity and disease enhancement factor: Mechanisms for complex dynamics in simple epidemiological models

Steindorf, Vanessa; Srivastav, Akhil Kumar; Stollenwerk, Nico; Kooi, Bob W.; Aguiar, Maíra

doi:10.1016/j.chaos.2022.112709

Cited by 11 publications

(25 citation statements)

References 29 publications

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“…The flowchart illustrating the two-infection model with coupled vector dynamics is presented in Figure 1, outlining the compartmental system of ordinary differential equations that describes the assumptions underlying dengue fever epidemiology. The set of ordinary differential equations (ODEs) for the deterministic twoinfection epidemiological system, as an extension of [34] to include explicit vector dynamics, is given by:…”

Section: The Two-infection Model With Coupled Vector Dynamicsmentioning

confidence: 99%

“…In this study we extend the model described in [34, 8] by incorporating the dynamics of a disease vector population. This extension explicitly involves the mosquito population, where, using standard incidence (as opposed to massaction incidence), susceptible human individuals become infected at a rate β upon encountering an infected mosquito.…”

Section: The Two-infection Model With Coupled Vector Dynamicsmentioning

confidence: 99%

“…From an analytical and theoretical perspective, the motivation of dengue fever epidemiology has also supported insights into the mechanisms required to generate complex dynamics in simple epidemiological models [34, 8, 32, 33, 31, 18]. However, the effect of the vector dynamics was not explicitly modeled but implicitly by seasonal infectivity.…”

Section: Introductionmentioning

confidence: 99%

“…Continuing the analysis, where complex dynamics were identified [34], including transcritical (sub-critical and supercritical) bifurcations (commonly known as forward and backward bifurcations in epidemiology), Hopf and global homo-clinic bifurcation curves, and the points where these curves intersect (Cusp and Bogdanov-Takens bifurcations), a step further is to introduce the explicit interaction with mosquito population into the model. Since dengue fever is transmitted to humans through the bite of an infected mosquito, this addition allows for a more comprehensive and biological representation of the host (human)-vector (mosquito)-pathogen cycle.…”

Section: Introductionmentioning

confidence: 99%

“…Since dengue fever is transmitted to humans through the bite of an infected mosquito, this addition allows for a more comprehensive and biological representation of the host (human)-vector (mosquito)-pathogen cycle. Therefore, this work aims to couple the vector population dynamics in a straightforward manner, as described in [2], to the model proposed in [34, 8]. The primary goal is to analyze the role of vector dynamics in the changes of mathematical bifurcation structures found in the SIRSIR-type model describing two subsequent infections and no strain structure of pathogens.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Bifurcation analysis of a two-infection transmission model with explicit vector dynamics

Srivastav,

Steindorf,

Guerrero

et al. 2023

Preprint

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The investigation of epidemiological scenarios characterized by chaotic dynamics is crucial for understanding disease spread and improving disease control strategies. Motivated by dengue fever epidemiology, in this study we introduce the SIRSIR-UV model, which accounts for differences between primary and secondary infections and explicit disease vector dynamics. Our analysis, employing nonlinear dynamics and bifurcation theory, provides key insights into how vectors contribute to the overall system dynamics. In this paper, the formalization of backward bifurcation using center manifold theory, computation of Hopf and global homoclinic bifurcation curves, and derivation of analytical expressions for transcritical and tangent bifurcations deepen the understanding. The observation of chaotic behavior with the inclusion of seasonal forcing in the vector population underscores the importance of considering external factors like climate in disease spread. Our findings align with those from previous models, emphasizing the significance of simplifying assumptions, such as implicit vector dynamics, when constructing models without vector control. This study brings significant insights to the mathematical modeling of vector-borne diseases, providing a manageable framework for exploring complex epidemiological scenarios and identifying key factors influencing disease spread. While the absence of strain structure may limit predictive power in certain scenarios, the SIRSIR-UV model serves as a starting point for understanding vector-borne infectious disease dynamics.

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Section: The Two-infection Model With Coupled Vector Dynamicsmentioning

confidence: 99%

Section: The Two-infection Model With Coupled Vector Dynamicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Bifurcation analysis of a two-infection transmission model with explicit vector dynamics

Srivastav,

Steindorf,

Guerrero

et al. 2023

Preprint

Self Cite

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Bifurcation analysis of a two infection SIR-SIR epidemic model with temporary immunity and disease enhancement

Aguiar,

Steindorf,

Srivastav

et al. 2024

Nonlinear Dyn

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In this paper we study a two infection SIR-SIR compartmental model, considering biological features described in dengue fever epidemiology. Due to a progressive loss of protective antibodies there is waning immunity in the first infection stage and disease enhancement or protection effects by the second infection stage. Bifurcation analysis reveals two codim-2 bifurcations as organizing centers. The unfolding of a cusp bifurcation describes the transition of the disease-free equilibrium into an endemic equilibrium by varying a parameter. These equilibria allow an analytical solution with explicit expressions which allow for a full geometrical interpretation of the occurring bifurcations related to stationary dynamics. A Bogdanov-Takens point is the starting point in the parameter space where oscillatory endemic dynamics occurs including a homoclinic connection. These findings bring additional insights on biological mechanisms able to generate rich and complicated dynamical behavior in simple epidemic models that are, so far, largely unexplored.

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Temporary Cross-Immunity as a Plausible Driver of Asynchronous Cycles of Dengue Serotypes

Fung,

Clapham,

Chisholm

2023

Bull Math Biol

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Modeling secondary infections with temporary immunity and disease enhancement factor: Mechanisms for complex dynamics in simple epidemiological models

Cited by 11 publications

References 29 publications

Bifurcation analysis of a two-infection transmission model with explicit vector dynamics

Bifurcation analysis of a two-infection transmission model with explicit vector dynamics

Bifurcation analysis of a two infection SIR-SIR epidemic model with temporary immunity and disease enhancement

Temporary Cross-Immunity as a Plausible Driver of Asynchronous Cycles of Dengue Serotypes

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