Mathematical model for Dengue with three states of infection

Doracelly Hincapie; Juan Ospina

doi:10.1117/12.919063

4 May 2012 Mathematical model for Dengue with three states of infection

Doracelly Hincapie, Juan Ospina

Proceedings Volume 8371, Sensing Technologies for Global Health, Military Medicine, Disaster Response, and Environmental Monitoring II; and Biometric Technology for Human Identification IX; 83710H (2012) https://doi.org/10.1117/12.919063
Event: SPIE Defense, Security, and Sensing, 2012, Baltimore, Maryland, United States

Abstract

A mathematical model for dengue with three states of infection is proposed and analyzed. The model consists in a system of differential equations. The three states of infection are respectively asymptomatic, partially asymptomatic and fully asymptomatic. The model is analyzed using computer algebra software, specifically Maple, and the corresponding basic reproductive number and the epidemic threshold are computed. The resulting basic reproductive number is an algebraic synthesis of all epidemic parameters and it makes clear the possible control measures. The microscopic structure of the epidemic parameters is established using the quantum theory of the interactions between the atoms and radiation. In such approximation, the human individual is represented by an atom and the mosquitoes are represented by radiation. The force of infection from the mosquitoes to the humans is considered as the transition probability from the fundamental state of atom to excited states. The combination of computer algebra software and quantum theory provides a very complete formula for the basic reproductive number and the possible control measures tending to stop the propagation of the disease. It is claimed that such result may be important in military medicine and the proposed method can be applied to other vector-borne diseases.

Citation Download Citation

Doracelly Hincapie and Juan Ospina "Mathematical model for Dengue with three states of infection", Proc. SPIE 8371, Sensing Technologies for Global Health, Military Medicine, Disaster Response, and Environmental Monitoring II; and Biometric Technology for Human Identification IX, 83710H (4 May 2012); https://doi.org/10.1117/12.919063

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