animals Review Caprine Arthritis Encephalitis Virus Disease Modelling Review Karina Brotto Rebuli, Mario Giacobini * and Luigi Bertolotti   Citation: Brotto Rebuli, K.; Giacobini, M.; Bertolotti, L. Caprine Arthritis Encephalitis Virus Disease Modelling Review. Animals 2021, 11, 1457. https://doi.org/10.3390/ani11051457 Academic Editor: Esperanza Gómez-Lucía and Ana Doménech Received: 20 April 2021 Accepted: 13 May 2021 Published: 19 May 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Dipartimento di Scienze Veterinarie, Università degli Studi di Torino, Largo Paolo Braccini 2, 10095 Torino, Italy; karina.brottorebuli@unito.it (K.B.R.); luigi.bertolotti@unito.it (L.B.) * Correspondence: mario.giacobini@unito.it Simple Summary: Mathematical modelling is used in disease studies to assess their economical impacts, as well as to better understand the epidemiological dynamics of the biological and en- vironmental 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. Abstract: 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. Keywords: CAE; CAEV; SRLV; epidemiological modelling; statistical modelling; diary produc- tion modelling 1. Introduction Caprine Arthritis Encephalitis (CAE) disease is a world-wide goat infectious disease [1–7] caused by Small Ruminant Lentiviruses (SRLV). Early phylogenetic stud- ies suggested that SRLV can be divided into five genetic groups, A to E [6]. Genotypes C and D as well subtypes A5 to A7 circulate only in goats; the subtype A2 circulates only in sheep, while subtypes A1, A3, A4, A6, B1 and B2 have been found in both species [8]. In goats, SRLV have a long incubation time and symptoms may be evident in only 10% of Animals 2021, 11, 1457. https://doi.org/10.3390/ani11051457 https://www.mdpi.com/journal/animals