Mathematical Modeling of the Interruption of the Transmission of Soil Transmitted Helminths Infections in Kenya

Abstract

Kenya, just like other countries with endemic soil-transmitted helminths (STH) infections, has conducted regular mass drug administration (MDA) program for the last five years among schoolaged children as a way of reducing STH infections burden in the country. However, the point of infection transmission interruption still remains unclear. TheWorld Health Organization (WHO) has set a target to eliminate STH by the year 2030. Thus, there is need for efficient and robust mathematical models that would enable STH program managers to develop reliable surveillance systems that meet sensitivity and specificity requirements for the endgame of STH elimination. The main objective of this thesis is to model the interruption of the transmission of STH infections in Kenya using a full age-structured deterministic model. Three mathematical models are formulated with the following assumptions; (i) no intervention for STH, (ii) only MDA intervention, and (iii) both MDA and water, sanitation and hygiene (WASH) interventions. In each model scenario, we were interested in comparing the impact of two outcomes, the mean worm burden levels in each of the host’s age group over a period of time and the transmission interruption period (elimination). The behaviour of these model outcomes was assessed based on different mix and plans of the projected interventions implementation. The models included a three age-structure of the human population which are of interest to the control programs, namely; pre-school age children (PSAC: 2 to 4 years), school-age children (SAC: 5 to 14 years), and adults (above 14 years). This complete categorization of the population enabled us to mimic a community-wide STH control program. The models incorporated a wide range of parameters that are thought to influence the transmission and elimination of STH infections in Kenya. These parameters are broadly grouped as; intervention-related, worm-related, population-related, and transmission and fecundity-related. vii Generally, these parameters can be often available, but with a considerable degree of uncertainty that may be counter-intuitive to the model behaviour especially when there are non-linearities in the multiple input-output relationships. Therefore, we performed a global sensitivity analysis (GSA) of the models based on a variance decomposition method: extended Fourier Amplitude Sensitivity Test (eFAST) to; (i) robustly compute sensitivity index (SI) for each parameter, (ii) rank the parameters in order of their importance (from most to least influential), and (iii) quantify the influence of each parameter on the model outcomes. Additionally, the study developed and analyzed an optimal control model, from the transmission interruption model, to obtain an optimal control strategy from a mix of three strategies using Pontryagin’s maximum principle. The model results demonstrated that the reduction of worm burden and elimination period was sensitive to and heavily depended on four parameter groups; drug efficacy, number of treatment rounds, MDA and WASH coverage. The analysis showed that for STH infections to be eliminated using MDA alone in a short time period of less than five years, 3-monthly MDA plan is desired. However, the complementation of MDA with WASH, at an optimal coverage level of 95%, was most effective and offered the best chances of eliminating these tenacious and damaging parasites. For STH control programs to effectively reach the STH endgame (elimination in the entire community), these key parameter groupings and strategy mix need to be targeted since they contribute to a strategic public health intervention.