Optimal control analysis of a transmission interruption model for the soil-transmitted helminth infections in Kenya

Abstract

Kenya is among the countries endemic for soil-transmitted helminthiasis (STH) with over 66 subcounties and over 6 million individuals being at-risk of infection. Currently, the country is implementing mass drug administration (MDA) to all the at-risk groups as the mainstay control strategy. This study aimed to develop and analyze an optimal control (OC) model, from a transmission interruption model, to obtain an optimal control strategy from a mix of three strategies evaluated. The study used the Pontryagin's maximum principle to solve, numerically, the OC model. The analysis results clearly demonstrated that water and sanitation when implemented together with the MDA programme offer the best chances of eliminating these tenacious and damaging parasites. Thus, we advocate for optimal implementation of the combined mix of the two interventions in order to achieve STH elimination in Kenya, and globally, in a short implementation period of less than eight years.

Keywords: Kenya; Mathematical model; Neglected tropical diseases; Optimal control; Soil-transmitted helminthiasis.

Graphical abstract

Fig. 1

Equilibrium points attained by each host in the absence of any intervention.

Fig. 2

Impact of the two interventions on the STH infections among each host. We assumed 80% drug efficacy, 75% treatment coverage, and 75% WASH coverage among all the hosts, the assumptions are as per the current WHO guidelines (WHO, 2011).

Fig. 3

Sensitivity analysis results of each parameter among the hosts computed using the eFAST method as outlined in equations (8), (9) and applied to model (1). The cut-off value above which a parameter was considered significant was 0.1 (denoted by the horizontal red dotted line). The further up a parameter span, the greater the influence it has on the model dynamics. Abbreviations: $Bp$, PSAC infection transmission rate; $Bc$, SAC infection transmission rate; $Ba$, adults infection transmission rate; $Mu$, mature worm mortality rate; $MuL$, infectious materials mortality rate; $np$, PSAC population proportion; $nc$, SAC population proportion; $na$, adults population proportion; $lambdap$, relative contributions by PSAC; $lambdac$, relative contributions by SAC; $lambdaa$, relative contributions by adults; $k$, over-dispersion parameter; $gma$, strength of density dependence of worm egg production; $Phi$, WASH effect; $Tau$, interval between treatment rounds per year; $gp$, proportion of PSAC treated; $gc$, proportion of SAC treated; $ga$, proportion of adults treated; $h$, drug efficacy.

Fig. 4

Strategy A: Prevention of STH using mass drug administration (MDA) as primary intervention. Consistent treatment coverage of 75% among each host group was assumed throughout the control period.

Fig. 5

Strategy B: Prevention of STH using provision of improved water and sanitation (WASH) as primary intervention. Consistent coverage of 75% for provision of improved WASH among each host group was assumed throughout the control period.

Fig. 6

Strategy C: Prevention of STH using both mass drug administration (MDA) and improved water and sanitation (WASH) as primary interventions. Consistent coverage of 75% for both MDA and WASH was assumed among each host group throughout the control period.