Modelling the impact of mass administration of ivermectin in the treatment of onchocerciasis (river blindness)

Figures & data

Figure 1. A compartmental representation of the epidemics and treatment of onchocerciasis. It is important to note that the model proposed here is an extension of the previous model studied in Omondi et al. (2017).

Figure 2. Comparison of the actual infected individuals and the estimated infected individuals.

Table 1. Estimated parameter values in the model for onchocerciasis case. The rates are given per day

Parameter	Range	Point value (assumed)	Source
$b_1$	0.0000819–0.001085	0.00009/N	Estimated
${\mu }_h$	0.0000391–0.0000548	0.000052	Central Intelligence Agency: The World Fact Book (2016), Ghana Statistical Service (2016)
${\beta }_h$	0–0.01	0.00198	Assumed
$\gamma$	0.00137–0.00365	0.00139	Animal Diversity Web (2016), Hopkins and Boatin (2011), Onchocerciasis (2016), Nguyen et al. (2005)
$\alpha$	0–1	[0.1, 0.65]	Turner et al. (2015), Winnen et al. (2002)
$\phi$	0.01–0.1	0.0015	Turner et al. (2015)
$\kappa$	0–1	0.0083	Assumed
$\rho$	0–0.1	0.001	Assumed
$\delta$	0–1	0.002	Assumed
$b_2$	0.0214–0.4	0.144/V	Assumed
${\beta }_v$	0–0.01	0.00079	Assumed
$\eta$	0.0714–0.1667	0.078	Animal Diversity Web (2016), Hopkins and Boatin (2011), How is Onchocerciasis Spread? (2016), Onchocerciasis (2016)
${\mu }_v$	0.0118–0.0714	0.068	Hopkins and Boatin (2011), Simulium spp. (2016)

Figure 3. Tornado plots of partial rank correlation coefficients (PRCCs) of the parameters that influence $R_0$ for the input parameters using the values in Table 1. Parameters with PRCC $>0$ increase $R_0$ when they are increased whereas parameters with PRCC $<0$ decrease $R_0$ when they are increased.

Figure 4. The Monte Carlo simulations for the three parameters with the greatest influence on the $R_0$: the transmission contact rate in humans, the transmission contact rate in the vector and the vector death rate for the input parameters using the values in Table 1 and 1,000 simulations per run. Eradication is only possible if the transmissibilities are extremely small or if the vector death rate is extremely high.

Figure 5. Eradication threshold for the three parameters with the greatest influence on $R_0$.

Figure 6. System behaviour for fixed and non-fixed mass administration of ivermectin with $\alpha =0.10,R_0=1.2412,b_1=0.0009,b_2=0.35,{\beta }_h=0.00562,{\beta }_v=0.00243,\phi =0.025,{\mu }_v=0.012$.

Figure 7. System behaviour for fixed and non-fixed mass administration of ivermectin with $\alpha =0.65,R_0=1.2412,b_1=0.0009,b_2=0.35,{\beta }_h=0.00562,{\beta }_v=0.00243,\phi =0.025,{\mu }_v=0.012$. Note that increasing $\alpha$ improves the outcome but does not lead to eradication.

Figure 8. System behaviour for fixed and non-fixed mass administration of ivermectin with $\alpha =0.10,R_0=0.9352,b_1=0.0009,b_2=0.35,{\beta }_h=0.00443,\phi =0.025,{\beta }_v=0.00175,{\mu }_v=0.012$. Non-fixed adminsitration may produce lower overall numbers of infected individuals, but the outcome is not predictable.

Figure 9. System behaviour for fixed and non-fixed mass administration of ivermectin with $\alpha =0.65,R_0=0.9352,b_1=0.0009,b_2=0.35,{\beta }_h=0.00443,\phi =0.025,{\beta }_v=0.00175,{\mu }_v=0.012$. Non-fixed administration may produces bursts of infection, even if the disease would be otherwise kept at low levels.

Figure 10. System behaviour for fixed and non-fixed mass administration of ivermectin with $\alpha =0.1,R_0=0.1181$ using parameter values in Table 1. Note that non-fixed administration may have a delaying or preventative effect on eradication.

Figure 11. System behaviour for fixed and non-fixed mass administration of ivermectin with $\alpha =0.65,R_0=0.1181$ using parameter values in Table 1. Increasing $\alpha$ hastens eradication, in both the fixed and non-fixed case.

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