Multiscale Modelling of Environmentally Transmitted Infectious Diseases

Abstract

In the field of mathematical biology, researchers are beginning to witness an overwhelming appreciation of multiscale modelling as an essential and suitable technique as opposed to a traditional single-scale modelling approach in predicting the dynamics of infectious disease systems. Yet, there is still a lack of evidence that generally indicates which among the different categories of multiscale models of infectious disease systems is more appropriate to use in multiscale modelling of infectious disease systems at different levels of their organization. This research study is the first of its kind to compare the suitability of the two fundamental categories of multiscale models of infectious disease systems which are nested multiscale models and embedded multiscale models in predicting disease dynamics with specific reference to environmentallytransmitted diseases. Two environmentally transmitted diseases are used as case studies, namely ruminant paratuberculosis and human ascariasis, to compare the two fundamental categories of multiscale models in predicting disease dynamics. The two environmentally-transmitted diseases considered in this study represent infectious disease systems with replication-cycle at microscale (i.e. ruminant paratuberculosis) and infectious disease systems without replication cycle at the microscale (i.e. human ascariasis). Firstly, the author develop a single-scale model at the host-level that we progressively extend to different categories of multiscale models that we later compare. The findings of this study (through both mathematical and numerical analysis of the multiscale models) are that for ruminant paratuberculosis which has a pathogen replication-cycle at the within-host scale both nested and embedded multiscale models can be used because both the models provide the same prediction of disease dynamics. However, for human ascariasis the findings are such that nested multiscale model is not appropriate in characterizing the disease dynamics, only the embedded is appropriate. Although the comparison of different categories of multiscale models in disease prediction carried out in this study are specific to paratuberculosis in ruminants and human ascariasis, the results obtained in this study are robust enough to be applicable to other infectious disease systems. Our results can be generalized to imply that for any level of organization of an infectious disease systems, if the disease has a replication cycle at the microscale, the nested multiscale and the embedded multiscle model provide the same accuracy in predicting disease dynamics. However, when the disease has no replication cycle at the microscale, only the embedded multiscle model is appropriate for predicting disease dynamics. In such a case, a nested multiscale model is inappropriate. We anticipate that this study will enable modelers to choose appropriate multiscale model category in the study of infectious diseases.