4th Summary- Mathematical Models for Epidemiological Studies, Dr. Mayte Cruz– Dept. of Mathematics-UPR -CayeyMath is logic, and at the end of the day no matter what people say; numbers don't lie. Epidemiological Studies

are known to be the cornerstone of disease control and incidence distribution. We began the workshop by

establishing mathematical models with the appropriate letters to indicate variables accepted in the scientific math

community. Some of these variables were β, which represented the infection rate and ∝ which meant the

proportionality in our mathematical model due to the related susceptibility and recurrent infection rates. It is

pivotal to establish the process these variables go through to help express values exponentially. The most

important part of our model is the basic reproductive number since it determines the secondary cases from

primal infection to a susceptible population, the spread of a disease will primarily depend on this variable since

the infection might grow stronger. In order to assist us for this mathematical modeling, we used bioinformatics,

we could easily do the calculations by hand one by one, yet the purpose of developed programs like the one we

used aim to make probabilities quicker. We used the Susceptible, Infected, Recovered (SIS) and Susceptible,

Exposed, Infected, Recovered (SEIR) models to understand how diseases might spread without taking into

consideration factors such as Network Connectivity (NC). This concept of NC has been one of the most pivotal

steps in modeling real world scenarios in mathematical terms , these could imply more than we think, since

hotspots may even be determined and the origin of the diseases could be established. All of these scientific

advancements could actually be what we need in order to understand how viral infections spread effectively in

order to avoid a worldwide contagion, which could occur in the future due to the present public undermining of

the situation. This workshop could actually be the cornerstone of investigations we might do in the near future

and understanding basic concepts of programming and modelling will aid us to attack problems from different

scenarios.