Title: Optimal Control for an Age-structured Model for the Transmission of HIV

We formulated an age-structured model for the transmission dynamics of HIV with differential infectivity: primary HIV infection, asymptomatic HIV infection, and acquired immunode- ficiency syndrome (AIDS) infection. The model without intervention strategies is completely analyzed. We compute the basic reproduction number which determines the outcome of the disease. We also compute equilibria and study their stability. The sensitivity analysis of the initial model parameters is performed (to determine the impact of control-related parameters on outbreak severity). Using optimal control theory, we determine the cost-effective balance of three interventions methods which min- imizes HIV-related deaths as well as the costs associated with intervention.

Title: Parameter and State Estimation using Real Data

This paper deals with the problem of the estimation of the unknown parameter and state variables that are not accessible to measurements using real data. More precisely, we use an auxiliary system called observer whose solutions tend exponentially to those of the original model. This observer that does not use the unknown parameters and uses only the available measurable data. In order, to validate the estimation results, numerical sim- ulations are conducted using real data to estimate the unknown parameters and variables. This allows to estimate the number of carriers that cannot be directly measured in a heterogeneous population and that play an important role on the transmission of the infection within a community of the African meningitis belt. We also provide a simple method to estimate the bacteria infection rate which is the parameter that is generally unknown in cholera disease.

Title: Be-CoDiS: A mathematical model to predict the risk of human diseases spread between countries. Validation and application to the 2014-15 Ebola Virus Disease epidemic.

Ebola virus disease is a lethal human and primate disease that currently requires a particular attention from the international health authorities due to important outbreaks in some Western African countries and isolated cases in the UK, the USA and Spain. Regarding the emergency of this situation, there is a need for the development of decision tools, such as mathematical models, to assist the authorities to focus their efforts in important factors to eradicate Ebola. In this work, we propose a novel deterministic spatialtemporal model, called Between-Countries Disease Spread (Be-CoDiS), to study the evolution of human diseases within and between countries. The main interesting characteristics of Be-CoDiS are the consideration of the movement of people between countries, the control measure effects and the use of time-dependent coefficients adapted to each country. First, we focus on the mathematical formulation of each component of the model and explain how its parameters and inputs are obtained. Then, in order to validate our approach, we consider two numerical experiments regarding the 20142015 Ebola epidemic. The first one studies the ability of the model in predicting the EVD evolution between countries starting from the index cases in Guinea in December 2013. The second one consists of forecasting the evolution of the epidemic by using some recent data. The results obtained with Be-CoDiS are compared to real data and other model outputs found in the literature.

Title: Models Meet the Real World: Lessons from Ebola in West Africa

Most infectious disease modeling is motivated by a desire to improve public health; however, modelers often struggle to effectively engage decision makers. I'll discuss two experiences working with US government personnel who were involved in decision-making during the West African Ebola epidemic. In both examples, a question-driven modeling approach was employed to identify appropriate goals for modeling projects, and model structures were tailored to questions identified through repeated discussion between modelers and public health stakeholders. I will summarize lessons learned by highlighting both barriers and keys to successful engagement and offer advice for actions that modellers can take to increase the public health impact of their research.

Title: Modeling Infectious Diseases of Africa

Among all regions of the world, the continent of Africa is characterized by the greatest infectious disease burden. In this talk, we will highlight some of the 25 deadliest diseases in human history and the top 10 most deadly diseases in Africa. In case studies, we will introduce mathematical models of malaria and Ebola, and illustrate how they might be used to mitigate outbreaks of these diseases and other pathogens.