Mathematical modelling of infectious diseases : COVID-19 and Malaria
(2023)
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- Abstract
- In COVID-19 modelling, we propose a simplified version of the well-known SIR compartmental model of infectious diseases. On several occasions, with optimized parameters and initial conditions, this time-invariant two parameter two-dimensional model is able to fit COVID-19 hospitalization data over several months with high accuracy (e.g., the root relative squared error is below 10% for Belgium over the period from 2020-03-15 to 2020-07-15). We also investigate the stochastic uncertainty, the parameter uncertainty and model uncertainty methods to produce confidence intervals for this proposed model. Moreover, we observed that, when the model is trained on a suitable three-week period around the hospitalization peak for Belgium, it forecasts the subsequent two months with mean absolute percentage error (MAPE) under 4%. We repeated the experiment for each French department and found 14 of them where the MAPE was below 20%. However, when the model is trained in the increase phase, it is less successful at forecasting the subsequent evolution. As for malaria modelling, we use a generalized linear models (GLM) with probability distributions: Poisson, negative binomial and Gaussian to forecast falciparum malaria incidence count per month considering monthly climatic variables: rainfall, average temperature and relative humidity, and the history of malaria incidence count in Dakar, Fatick and Kedougou, three different endemic regions of Senegal. Forecasting algorithm methods are developed. In protocol (1): the meteorological explanatory variable Xj is taken at time t − ℓj, where t represents the time of the forecasts, ℓj is the lag in Xj that maximizes its correlation with the malaria incidence. In protocol (2): the meteorological explanatory variables are assumed to be available at time t. In addition, a saturation method is introduced on the rainfall variable to remedy some overestimations observed during the forecasts. Results show that the protocol (2) outperforms the protocol (1) with low MASE’s in the test periods: 0.94 in Dakar, 0.92 in Fatick and 0.8 in Kedougou. These values indicate an excellent accuracy of the model with our datasets. Introducing the saturated rainfall has reduced by 4% in the sense of MARE the overestimation occurring at the end of 2015 in Dakar, only with protocol (1).
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Diao, O. (2023). Mathematical modelling of infectious diseases : COVID-19 and Malaria. https://hdl.handle.net/2078.5/102260