Abstract
Simple SummaryMathematical modelling is used in disease studies to assess their economical impacts, as well as to better understand the epidemiological dynamics of the biological and environmental factors associated with disease spreading. For an incurable disease such as Caprine Arthritis Encephalitis, this knowledge is extremely valuable. However, the application of modelling techniques to study this disease has not been significantly explored in the literature. The purpose of the present work was to review the published studies, highlighting their scope, strengths and limitations, as well to provide ideas for future modelling approaches for this disease. The reviewed studies were divided into two major themes. The first is epidemiological modelling, which use mathematical models which equations describe the disease dynamics over time. Inside this group, the articles differ in considering or not considering the sexual transmission component. The second major theme is statistical modelling, which correlates the disease with biological and environmental factors to quantify its risks and impacts. Inside this group, the articles include models for dairy production, for risk factors of the disease and for Caprine Arthritis Encephalitis being a risk factor for other diseases. Finally, the present work concludes with further suggestions for modelling studies on Caprine Arthritis Encephalitis.Mathematical modelling is used in disease studies to assess the economical impacts of diseases, as well as to better understand the epidemiological dynamics of the biological and environmental factors that are associated with disease spreading. For an incurable disease such as Caprine Arthritis Encephalitis (CAE), this knowledge is extremely valuable. However, the application of modelling techniques to CAE disease studies has not been significantly explored in the literature. The purpose of the present work was to review the published studies, highlighting their scope, strengths and limitations, as well to provide ideas for future modelling approaches for studying CAE disease. The reviewed studies were divided into the following two major themes: Mathematical epidemiological modelling and statistical modelling. Regarding the epidemiological modelling studies, two groups of models have been addressed in the literature: With and without the sexual transmission component. Regarding the statistical modelling studies, the reviewed articles varied on modelling assumptions and goals. These studies modelled the dairy production, the CAE risk factors and the hypothesis of CAE being a risk factor for other diseases. Finally, the present work concludes with further suggestions for modelling studies on CAE.
Highlights
Caprine Arthritis Encephalitis (CAE) disease is a world-wide goat infectious disease [1–7] caused by Small Ruminant Lentiviruses (SRLV)
Since there is no cure for CAE, it does not make sense to model the Recovered compartment and the models discussed in this work have only the Susceptible and the Infected compartments
According to the results presented in the article, the serological status of a goat is linked to its parity: the higher the parity, the greater the probability of CAE infection; the probability of infection in 1 year old goats was lower by 84% and in 2 years old goats by
Summary
Caprine Arthritis Encephalitis (CAE) disease is a world-wide goat infectious disease [1–7] caused by Small Ruminant Lentiviruses (SRLV). A very known example is the Susceptible-Infected-Recovered (SIR) model [17] in the epidemiological field In this model, the individuals in the population are divided into compartments according to the their status of the disease. Once the equations of the model and the initial conditions are defined, the mathematical behaviour of the system is deterministic It is studied by techniques like the analysis of its equilibra points (set of solutions M such that x (0) in M =⇒ x (t) ∈ M ∀ t ∈ R), numerical simulations, amongst others. The stochastic nature of the model, in this case, is represented by the residual error term (e) that adds a Normal distribution perturbation to the model outcome Another important aspect of the statistical modelling is that the values of the parameters themselves have an uncertainty.
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