Workshop on Modelling of Infectious Diseases Dynamics

There is no “one size fits all” intervention for malaria elimination due to the spectrum of available sub-optimal interventions acting at different stages of the parasite life-cycle and the heterogeneous transmission landscape. Every district of every country has its own unique challenges, conditions and solutions. Mathematical modelling is the best available approach for combining the many interacting factors that must be considered. In a recent project bespoke mathematical and economic models were developed in parallel with training a new group of modellers based in their own countries around the World. The resulting research demonstrates that modelling can be used to support all aspects of the World Health Organization Global Technical Strategy for Malaria within the countries where the disease persists.

In this work we analyse results obtained when considering individuals as mobile agents, which can interact for a period of time that depends on the agent dinamics. In this way, as the probability of disease transmission depends on this contact time, the spatial dynamics will strongly influence the disease spreading. Surprisingly, the size of the endemic population will have three different regimes depending on the speed: elimination of the disease if it is very low, inversely proportional to the speed for intermediate values, and a final case that depends on the contact. Moreover, we recently found that these last two regimes also depend heavily on the type of the dynamics (ballistic or diffusive). The same goes for the critical speed at which the disease disappears.

The prediction of dengue outbreaks based on disease surveillance is  a very hard problem and a lot of work  had been done in this direction. In this talk, we present two studies with different techniques to partially address the problem. First, with the data for the state of São Paulo, we propose a time-scale separation to adjust the parameters and explore some cell phone data. In the second, using the incidence data for the state of Rio de Janeiro, inspired by the work of Saba, Vale, Moret and Miranda, we propose a way to identify a correlation network that would capture the space connections between the outbreaks.

Brazilian Spotted Fever is an infectious, acute febrile disease, of varying severity, whose clinical presentation in humans can vary from mild and atypical forms to severe forms, with a high lethality rate. It is caused by a bacterium of the genus Rickettsia (Rickettsia rickettsii) and transmitted by ticks of the genus Amblyomma. In some locations in the state of São Paulo, the capybara (Hydrochoerus hydrochaeris) participates in the disease cycle as an amplifier of the etiologic agent after contact with infected ticks. As a result of this possible participation of the capybara in the cycle and the eventual need to carry out population management of the species, the State of São Paulo, through the Secretariat of Infraestructure and Environment and the Secretariat of Health, published Resolution SMA-SES No. 01/2016, which provides the -œTechnical guidelines for the surveillance and control of Brazilian Spotted Fever in the State of São Paulo - classification of areas and recommended measures -, which establishes criteria for the management of capybaras in situations where this species is associated with the risk of transmitting Brazilian Spotted Fever to humans.

Artificial Neural Networks (ANNs) have been demonstrated to be an excellent method for dealing with various kind of tasks, such as image classification and natural language processing. These ANNs can also be used for regression since they are considered to be an universal function approximator, thanks to it's great capacity of dealing with non linear tasks. On the other hand, Floris Takens have shown to be possible to access and reconstruct the underlying dynamics of a system in the space state, starting from a single measured time series. In other words, Takens' theorem says it is possible to get information of a higher dimensional system from vectors build from a one-dimensional time series. This enables better time-series representations that can be fed into the ANNs. In this work, I will apply Echo State Networks (ESNs), one among the types of ANNs, to make forecasts of the dynamics of physical systems, such as Lorenz, Fokker-Planck and Vlasov Equations. I also pretend to apply these ESNs, together with Takens Vectors, into real time series, such as epidemics spread and financial series.

In my presentation I will comment on the preliminary advances and results that we have in the Centro de Estudios de Variabilidad y Cambio Climático (CEVARCAM, FICH-UNL), where since last year a group of researchers is being formed in the line of assessing the impact of climate change on the health of the population. Particularly we study the incidence of infectious diseases and their relationship with different hydroclimatic and environmental indicators in Northeast Argentina. I work in deterministic modelling of infectious diseases while another partner works in stochastic modeling.

Globalization has created complex problems that can no longer be adequately understood and mitigated using traditional data analysis techniques and data sources. As such, there is a need for the integration of nontraditional data streams and approaches such as social media and machine learning to address these new challenges. In this talk, I will discuss how our team is applying approaches from the weather forecasting community including data collection, assimilating heterogeneous data streams into models, and quantifying uncertainty to forecast influenza and other infectious diseases. In addition, I will demonstrate that although epidemic forecasting is still in its infancy, it’s a growing field with great potential and mathematical modeling will play a key role in making this happen.