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Dynamical behavior and bifurcation analysis for a theoretical model of dengue fever transmission with incubation period and delayed recovery
Populations and Evolution · Submitted 10 Mar 2025
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The stability analysis of the model revealed that various dynamical behaviour can be observed depending on delay parameters, where in particular the effect of delay in the recovery time of infectious individuals may lead to substantial changes in the dynamics.
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The abstract, sentence by sentence
As offered by the World Health Organisation (WHO), close to half of the population in the world's resides in dengue-risk zones. Dengue viruses are transmitted to individuals by Aedes mosquito species infected bite (Ae. Albopictus of Ae. aegypti). These mosquitoes can transmit other viruses, including Zika and Chikungunya. In this research, a mathematical model is formulated to reflect different time delays considered in both extrinsic and intrinsic incubation periods, as well as in the recovery periods of infectious individuals. Preliminary results for the non-delayed model including positivity and boundedness of solutions, non-dimensionalization and equalibria analysis are presented. The threshold parameter (reproduction number) of the model is obtained via next generation matrix schemes. The stability analysis of the model revealed that various dynamical behaviour can be observed depending on delay parameters, where in particular the effect of delay in the recovery time of infectious individuals may lead to substantial changes in the dynamics. The ideas presented in this paper can be applied to other infectious diseases, providing qualitative evaluations for understanding time delays influencing the transmission dynamics.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | As offered by the World Health Organisation (WHO), close to half of the population in the world's resides in dengue-risk zones. | background 1.00 | 0.03 | 0.02 | asserted 0.98 |
| s1 | Dengue viruses are transmitted to individuals by Aedes mosquito species infected bite (Ae. | background 1.00 | 0.04 | 0.02 | asserted 0.99 |
| s2 | Albopictus of Ae. aegypti). | background 1.00 | 0.04 | 0.02 | asserted 0.51 |
| s3 | These mosquitoes can transmit other viruses, including Zika and Chikungunya. | background 1.00 | 0.06 | 0.02 | asserted 0.91 |
| s4 | In this research, a mathematical model is formulated to reflect different time delays considered in both extrinsic and intrinsic incubation periods, as well as in the recovery periods of infectious individuals. | method 0.60 | 0.94 | 0.05 | asserted 0.99 |
| s5 | Preliminary results for the non-delayed model including positivity and boundedness of solutions, non-dimensionalization and equalibria analysis are presented. | contribution 0.54 | 0.92 | 0.04 | asserted 0.99 |
| s6 | The threshold parameter (reproduction number) of the model is obtained via next generation matrix schemes. | method 0.70 | 0.93 | 0.05 | asserted 1.00 |
| s7 | The stability analysis of the model revealed that various dynamical behaviour can be observed depending on delay parameters, where in particular the effect of delay in the recovery time of infectious individuals may lead to substantial changes in the dynamics. | result 0.97 | 0.94 | 0.75 | hedged possibility 0.52 |
| s8 | The ideas presented in this paper can be applied to other infectious diseases, providing qualitative evaluations for understanding time delays influencing the transmission dynamics. | interpretation 0.69 | 0.24 | 0.13 | hedged possibility 0.70 |
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Original abstract
As offered by the World Health Organisation (WHO), close to half of the population in the world's resides in dengue-risk zones. Dengue viruses are transmitted to individuals by Aedes mosquito species infected bite (Ae. Albopictus of Ae. aegypti). These mosquitoes can transmit other viruses, including Zika and Chikungunya. In this research, a mathematical model is formulated to reflect different time delays considered in both extrinsic and intrinsic incubation periods, as well as in the recovery periods of infectious individuals. Preliminary results for the non-delayed model including positivity and boundedness of solutions, non-dimensionalization and equalibria analysis are presented. The threshold parameter (reproduction number) of the model is obtained via next generation matrix schemes. The stability analysis of the model revealed that various dynamical behaviour can be observed depending on delay parameters, where in particular the effect of delay in the recovery time of infectious individuals may lead to substantial changes in the dynamics. The ideas presented in this paper can be applied to other infectious diseases, providing qualitative evaluations for understanding time delays influencing the transmission dynamics.
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