Multi-Scale Modelling of Vector-Borne Diseases

Abstract

In this study, we developed multiscale models of vector-borne diseases. In general, the transmission of vector-borne diseases can be considered as falling into two categories, i.e. direct transmission and environmental transmission. Two representative vector-borne diseases, namely; malaria which represents all directly transmitted vector-borne diseases and schistosomiasis which represents all environmentally transmitted vector-borne diseases were studied. Based on existing mathematical modelling science base, we established a new multiscale modelling framework that can be used to evaluate the effectiveness of vector-borne diseases treatment and preventive interventions. The multiscale models consisted of systems of nonlinear ordinary differential equations which were studied for the provision of solutions to the underlying problem of the disease transmission dynamics. Relying on the fact that there is still serious lack of knowledge pertaining to mathematical techniques for the representation and construction of multiscale models of vector-bone diseases, we have developed some grand ideas to placate this gap. The central idea in multiscale modelling is to divide a modelling problem such as a vector-bone disease system into a family of sub-models that exist at different scales and then attempt to study the problem at these scales while simultaneously linking the sub-models across these scales. For malaria, we formulated the multiscale models by integrating four submodels which are: (i) a sub-model for the mosquito-to-human transmission of malaria parasite, (ii) a sub-model for the human-to-mosquito transmission of malaria parasite, (iii) a within-mosquito malaria parasite population dynamics sub-model and (iv) a within-human malaria parasite population dynamics sub-model. For schistosomiasis, we integrated the two subsystems (within-host and between-host sub-models) by identifying the within-host and between-host variables and parameters associated with the environmental dynamics of the pathogen and then designed a feedback of the variables and parameters across the within-host and between-host sub-models. Using a combination of analytical and computational tools we adequately accounted for the influence of the sub-models in the different multiscale models. The multiscale models were then used to evaluate the effectiveness of the control and prevention interventions that operate at different scales of a vector-bone disease system. Although the results obtained in this study are specific to malaria and schistosomiasis, the multiscale modelling frameworks developed are robust enough to be applicable to other vector-borne diseases.