OUTLINEOUTLINE LAST SEMESTER’S RESULTS

METAPOPULATION NETWORKOBJECTIVESRESEARCH QUESTIONSMETHODOLOGYTRAFIC FLOWTHE MOBILITY MODELMATHEMATICAL MODEL ACKNOWLEDGMENTSFUTURE WORKREFERENCES

AVIAN FLU TYPE A-H5N1AVIAN FLU TYPE A-H5N1

Avian flu is a zoonotic infectious disease of birds caused by viruses of the Type A-H5N1.

What are zoonotic diseases?Zoonotic Disease are contagious diseases

spread between animals (domestic or wild) and humans.

SQUEMATIC OF THE MATHEMATICAL MODEL

SQUEMATIC OF THE MATHEMATICAL MODEL

Previous ResultsPrevious Results

We found that as we vaccinate at least 10% of the population the epidemic can be mitigated but if we at least vaccinate 30% we can lower the epidemic considerably.

Also, as we vaccinate earlier in time before the epidemic start it course we can lower the death, the amount of time the epidemic lasts and the size.

RESEARCH QUESTION: What mechanisms are effective to contain a

potential Avian A-H5N1 epidemic?

RESEARCH QUESTION: What mechanisms are effective to contain a

potential Avian A-H5N1 epidemic?

OBJECTIVESOBJECTIVESDetermine the potential outbreaks of this disease in Puerto Rico implement a networking approach in a simpler SIR model.

Using the estimated parameter values to predict metapopulation dynamics and networked metapopulation in two cities of Puerto Rico.

RESEARCH QUESTIONSRESEARCH QUESTIONS

Which dynamics of disease spreading affect an outbreak among cities?

What mechanisms are effective to contain a potential Avian A-H5N1 epidemic among cities?

METAPOPULATIONMETAPOPULATIONWHAT MEANS METAPOPULATION

MODEL?

A metapopulation model consists of a group of interacting spatially separated populations of the same species.

The dynamics of metapopulation systems is a set of differential equations coupled together.

METHODOLOGYMETHODOLOGYWe implemented the

simpler mobility model for two cities in Puerto Rico on a SIR-type model to investigated the potential outbreak of this disease in the area of Cayey and Aibonito.

CayeyCayey

AibonitoAibonito

Individual Mobility

N1= 48,119

N2= 25,900S I R

TRAFFIC FLOW BETWEEN CITIES

TRAFFIC FLOW BETWEEN CITIES

PARAMETERSPARAMETERS

Parameters Definitions Values

βp Infectious rate for chickens 2.5

βh

Infectious rate for humans - humans

interaction0.5

βhp

Infectious rate for humans - chickens

interaction0.2

�h

Lower infectivity for the interaction

between exposed and susceptible humans

0.95

αh Recovery rate for humans 0.1

Parameter values of the mathematical model

Parameter values of the mathematical modelParameters Definitions Values

P1

Instant Transportation for the city of Aibonito

Estimation

P2

Instant Transportation for the city of Cayey

Estimation

δhDeath rate due to

infection in humans 0.005

µhDemography-birth rate and mortality

Estimation

PARAMETERSPARAMETERS

MOBILITY MODELMOBILITY MODEL

SPSP IPIP RPRP

S1S1 I1I1 R1R1

S2S2 I2I2 R2R2

AIBONITOAIBONITO

CAYEYCAYEY

POULTRYPOULTRY

MATHEMATICAL MODELEQUATIONS FOR TWO CITIES

MATHEMATICAL MODELEQUATIONS FOR TWO CITIES

Epidemic dynamic for the human population in CayeyEpidemic dynamic for the human population in Cayey

Epidemic dynamic for the human population in Aibonito

Epidemic dynamic for the human population in Aibonito

RATE OF INFECTIONRATE OF INFECTION

RATE OF INFECTIONRATE OF INFECTION

FUTURE WORKFUTURE WORKMathematical analysisImplement different parameter values for the mathematical mobility model.Work on the basic reproductive number values of our coupled model.

Computational analysisWork on simulations to study the dynamics of the epidemic in different scenarios.Implement a networking approach in the model to include the spread of the disease in different towns in Puerto Rico.

Extension of the model to more cities

ACKNOWLEDGMENTSACKNOWLEDGMENTSScience is the basis of all research and implementing

the importance of mathematics can make big changes which is why I acknowledge:

University of Puerto Rico at Cayey.

I thank God and my mentor Dr. Mayteé Cruz-Aponte, for giving me the opportunity to work on this important investigation.

The Rise Program of Bio-medics to provide me with the opportunity to present this important research and implement it in other places.

ANY QUESTIONS ABOUT THE PROPOSAL?

ANY QUESTIONS ABOUT THE PROPOSAL?

REFERENCESREFERENCES1. Avian Influenza A H5N1 infection in Humans, “The Writing Commite of the World

Health Organization (WHO), Consultation on Human Influenza A/H5”; John H. Biegel, M.D., National Institute of Allergy and Infectious Diseases, Jeremy Farrar, September 29, 2005.

2. Human Influenza A H5N1, virus related to a highly pathogenic avian influenza virus, Eric C J Class, Albert D M E Osterhaus, Ruud van Beek, Jan C De Jong ; THE LANCET Vol. 351; February 14, 1998.

3. Experimental infection of highly pathogenic avian influenza virus H5N1 in blackheaded gulls (Chroicocephalus ridibundus), Antonio Ramis, Geert van Amerongen, Marco van de Bildt, Loneke Leijten, 2 March 2014.

4. Computational analysis and determination of a highly conserved surface expose segment in H5N1 avian flu and H1N1 swine flu neuraminidase, Ambarnil Ghosh, Ashesh Nandy and Nandy Papiya, Ghosh et al. BMC Structural Biology 2010, 10:6.

5. Standardization of a molecular detection method of highly pathogenic avian influenza virus H5N1, Maricela Montalvo-Corral, Monica Resendiz, Gerardo Santos-López, Verónica Vallejo Ruiz, Julio Reyes- Leyva and Jesus Hernandez:, Acta Bioquim Clin Latinoam 2009: 43(1): 49-52.

6. Comparison of ARIMA and Random Forest time series models for prediction of avian influenza H5N1 outbreaks, Michael J Kane, Natalie Price, Matthew Scotch and Peter Rabinowitz.

THANKS FOR YOUR ATTENTION

THANKS FOR YOUR ATTENTION

“The essence of mathematics is its freedom” George Cantor