EPIDEMIOLOGICAL MODEL OF DENGUE IN PUERTO RICOAlmarely L. Berrios Negrón, Carlo S. González Acevedo, Ana M. Rodríguez López

Mentor: Dr. Mayteé Cruz-Aponte;Department of Mathematics–Physics

University of Puerto Rico – Cayey

INTRODUCTION

MATHEMATICAL MODEL

SIMULATIONS AND PRELIMINARY RESULTS

SELECTED REFERENCES

Parameters Description

1/ωx 5 – 10 days Days the host is infected

βv 0.75 Probability of effective contact for vector

βh 0.50 Probability of effective contact for humans

1/αx 4 – 10 days Days of incubation in host

1/px 8 – 12 days Days of disease incubation in vector

δx 0.01 = 1% Probability of death by the disease

Phases Febrile Phase 2 – 7 daysCritical Phase Occurs on days 3 - 7

Where x will indicate a distinct type of Dengue.

Distinct Infection Period for the Host

Distinct Incubation Period for the Host Distinct Incubation Period for the VectorA B

C

All simulations use the parameters as given in the Mathematical Model section varying the incubation period of the host 1/αx (for Figure A), the incubation period of the vector 1/px (Figure B) and the infection period of the host 1/ωx (Figure C).

Dengue is the most rapidly spreading mosquito-borne viral disease in the world. It’s transmitted by several species of mosquito within the genus Aedes, principally Aedes aegypti. There are four distinct serotypes of the dengue virus (DEN 1, DEN 2, DEN 3 and DEN 4). Symptoms appear in 2 – 7 days (on an average 4 – 7 days) after the infective bite. Dengue fever is a flu - like illness that affects infants, young children and adults and there is no specific treatment for it. Severe dengue is a potentially lethal complication but early clinical diagnosis and careful clinical management by experienced physicians and nurses often save lives. More than 70% of the disease burden is in South-East Asia and the Western Pacific. In Latin America and the Caribbean, the incidence and severity of disease have increased rapidly in recent years. In Puerto Rico, an estimated yearly mean of 580 years per million population were lost to disability adjusted life from dengue infections between 1984 and 1994. Urbanization, rapid movement of people and goods, favorable climatic conditions and lack of trained staff has all contributed to the global increase of dengue. On this research, we plan to create an epidemiological model to describe mathematically the infection in Puerto Rico and create simulations to understand the spreading of the disease.

1. Samat, N. A., & Percy, D. F. Numerical Analysis of the SIR-SI Differential Equations with Application to Dengue Disease Mapping in Kuala Lumpur, Malaysia.

2. World Health Organization, Special Programme for Research, Training in Tropical Diseases, World Health Organization. Department of Control of Neglected Tropical Diseases, World Health Organization. Epidemic, & Pandemic Alert. (2009). Dengue: guidelines for diagnosis, treatment, prevention and control. World Health Organization.

3. Semana 40 - 43 del 22 - 28 de octubre del 2014. Informe Semanal de Vigilancia del Dengue. Departamento de Salud de Puerto Rico Informe. http://www.salud.gov.pr/dengue/CDC%202014/Informe%20Dengue%20Semana%2040%202014.pdf. Accesado, 24 de noviembre de 2014.

A

B

C

Images from salud.gov.pr Weekly Dengue Report from week 40 (October 1 - 7, 2014), report as of November 19, 2014. Weekly Surveillance Report for Chikungunya. Department of Health of Puerto Rico.

We thank the BRIC program and the University of Puerto Rico at Cayey for the opportunity to conduct this research and our mentor Dr. Mayteé Cruz-Aponte for guiding us.

Acknowledgments

• Focus on working on the model and searching for more information about the infection to adjust the parameters for our model.• Describe epidemiologically with the use of our model the popular infection called Dengue.• Further on, we need to establish numerical and statistical values for our model and analyze them so we can incorporate our

research into a mathematical structure.

FUTURE WORK

𝑆𝑣 𝐿𝑣 𝐼𝑣

𝑆𝐻 𝐿𝐻 𝐼𝐻 𝑅𝐻

Using 1/px = 8 days, 1/ωx = 10 days and varying 1/αx = 5, 7 and 10 days we observe that as the incubation period of the host increases the epidemic start days later and the peak of the epidemic is lower and occurs later but the epidemic duration is similar for all.

Using 1/ωx = 5 days, 1/αx = 10 days and varying 1/px = 8, 10 and 12 days we observe that as the incubation period of the vector increases the epidemic start very few days later and the pick is not significantly lower, the epidemic duration is similar for all but this changes are not significant.

Using 1/px = 10 days, 1/αx = 7 days and varying 1/ωx = 5, 7 and 10 days we observe that as the infection period of the host increases the epidemic start a few days later but there is a significant change in the epidemic duration, the peak height and overall the final size of the epidemic (i.e. the number of people infected overall.