Mathematical Models for Predicting and Monitoring the Impact of COVID-19 in Rwanda

A: Background: To control human and animal diseases, the mathematical modeling and simulation are very important tools since that they can provide projections of the likely future, provide descriptions of the natural history of infections at a population and individual level, and provide insights into the impact of possible interventions. The dynamical biological processes are better modeled by means of systems of deterministic differential equations (ordinary (ODE), partial (PDE), or delay (DDE). Scientists have contributed a lot in modelling the spread of epidemics and the plans for controlling the spread. The development of the mathematical model of COVID-19 should take into account the known specific characteristics of this new disease. In Rwanda, the flow of COVID-19 can be modeled using deterministic mathematical compartmental epidemic models, stochastic differential equations (SDEs) and network models B. Goal and Objectives The goal of this project is to develop a mathematical modeling framework for predicting and monitoring the COVID-19 pandemic in Rwanda. Developed models will help in understanding the disease transmission dynamics, as well as give insights into the effectiveness of control strategies by providing forecasts of the disease burden on the country and hence of eventual health care saturation, infrastructure and facilities needs hospitals, in quarantine centers. Objectives: 1. Build a deterministic mathematical model able to capture the dynamic transmissions of COVID-19 in Rwanda; 2. Build a stochastic model able to capture the inherent random, and uncertain factors influencing the spread and control of COVID-19 in Rwanda; 3. Develop a graph-based network model for COVID-19 propagation in Rwanda based on a random network of contacts between individuals; 4. Develop a statistical framework to analyse the response and impact of COVID-19 pandemic in Rwanda from a multi-discipline perspective and investigate the eventual situation of endemicity of COVID-19; 5. Connect the developed models to existing database through a well-designed App to automate data processing and produce a dashboard to allow quick actions from health care authorities. C. Methods The model will be constructed by using deterministic, stochastic and networking approaches.  Study design: The total effective Rwandan population size will be divided into eight compartments: Susceptible (S), Exposed (E), Quarantine (Q), Infectious (I), Undocumented infected (Iu), Hospitalized (H), Recovered (R) and Dead (D); that is the mathematical model SEQIHRD. All the compartments will be linked by parameters to be estimated using data. Two 30 cases will be studied (1) the population is assumed to be closed (there is a pure confinement or lockdown) and (2) the post lockdown where the population is free to move even borders are open, i.e. the population is living with COVID-19.  Data collection: secondary data will be used. They will be collected from clinical records of RBC (Rwanda Biomedical Centre) and other well established data bases. During the analysis of post lockdown, researchers will be interested in effective measures used to contain the outbreak. Therefore, primary data will be collected using questionnaire that will be designed according to the needed variables.  Epidemiological models: Through the transfer diagram, the compartmental mathematical model SQEIHRD will be developed in form of Ordinary differential equations by considering the special characteristics of the pandemic in Rwanda. The deterministic model may then be extended into a stochastic model and network model by taking into account the random fluctuations observed along the time of the outbreak.  Model parameters estimation and validation: The estimation of parameters will be done using Least Square Method and others may be found from literatures or medical experiments. Once the model is validated as accurate it will be used to study different scenario specified in the call. It will be used for monitoring and prediction using the dashboard to allow quick actions from authorities in charge of COVID-19. Furthermore, a statistical model capturing all the collected data can be identified and used for prediction. D: Expected Outcomes are:  Improved scientific understanding of the disease  Inform decision making on easing lockdown measures  Inform policy makers and health care professionals for post-corona strategies  Preparedness for eventual future infectious diseases