Modeling the Stochastic Dynamics of Influenza Epidemics with Vaccination Control, and the Maximum Likelihood Estimation of Model Parameters
Contribution to Book
Mathematical Modelling in Health, Social and Applied Sciences
This study presents a family of stochastic models for the dynamics of influenza in a closed human population. We consider treatment for the disease in the form of vaccination and incorporate the periods of effectiveness of the vaccine and infectiousness for the individuals in the population. Our model is a SVIR model, with trinomial transition probabilities, where all individuals who recover from the disease acquire permanent natural immunity against the strain of the disease. A special SVIR model in the stochastic family based on correlated vaccination and infection probabilities at any instant is presented. The methods of maximum likelihood and expectation–maximization algorithm are applied to find estimates for the parameters of the chain. Moreover, estimators for some special epidemiological control parameters, such as the basic reproduction number, are computed. A numerical simulation example is presented to find the MLE of the parameters of the model.
Wanduku, Divine, Charles C. Newman, Omotomilola Onaopemipo Jegede, Broderick O. Oluyede.
"Modeling the Stochastic Dynamics of Influenza Epidemics with Vaccination Control, and the Maximum Likelihood Estimation of Model Parameters."
Mathematical Modelling in Health, Social and Applied Sciences: 23-72 Singapore: Springer Nature.
doi: 10.1007/978-981-15-2286-4_2 isbn: 978-981-15-2286-4
© Springer Nature Singapore Pte Ltd. 2020