Optimal control of malaria: combining vector interventions and drug therapies

Malaria Journal

Table 1 Parameter definitions and values. Disease parameters use P. falciparum estimates

Parameter	Description	Default value	Notes
N	Host population	$2\times 10^5$	Variable
$k^*$	Vectors per host at equilibrium	2	But can be as high as 200 [69, 71,72,73]
b	Mosquito bite rate	0.5 per day	[74]
a	Vector to human transmission efficiency	0.07	[75]
c	Human to vector transmission efficiency	0.1	[76, 77]
$\gamma$	Malaria recovery rate	1/14 per day	Variable, assuming a 2-week average with conventional treatment
s	Artemisinin-enhanced recovery rate	$\frac{1}{3}\ln {10}$ per day	$90\%$ success rate over 3 days [5, 78]
$\rho$	Per adult female oviposition rate	16 per day	[79,80,81]
m	Larval maturation rate	0.1 (0.05, 0.17)	[82]
$\mu _A$	Adult mosquito death rate	$\ln \frac{10}{9}$ per day	[73, 76, 77, 83, 84], chosen to be conservative
$\mu _L$	Density-independent larval death rate	0.03 per day	[85]
$\beta$	Strength of density dependence	0.9	Varies from $\beta <1$ for contest to $\beta >1$ for scramble
$\nu$	Scale of larval density-dependence	Eq. (4)	Ensures $A^* = k^* N$
$\theta _1$	Cost per infected individual	$11.43 \gamma$ $(3.03 \gamma , 37.12 \gamma )$ $ per day	Mean (min, max) from [61]
$\theta _2$	Cost of artemisinin therapy	$\frac{4.61}{3}$ $(\frac{3.96}{3}, \frac{5.57}{3})$ $ per day	Mean (min, max) from [5] assuming 3 day treatment
$\theta _3 \times 10^4$	Cost per $10^4$ insects released	9.11 (1.93, 25.36) $ per day	Mean (min, max) from [43, 86,87,88,89, 89, 90]
$\psi$	Future discounting factor	0.1/365 per day	Variable

ISSN: 1475-2875

Parameter	Description	Default value	Notes
N	Host population	\(2\times 10^5\)	Variable
\(k^*\)	Vectors per host at equilibrium	2	But can be as high as 200 [69, 71,72,73]
b	Mosquito bite rate	0.5 per day	[74]
a	Vector to human transmission efficiency	0.07	[75]
c	Human to vector transmission efficiency	0.1	[76, 77]
\(\gamma\)	Malaria recovery rate	1/14 per day	Variable, assuming a 2-week average with conventional treatment
s	Artemisinin-enhanced recovery rate	\(\frac{1}{3}\ln {10}\) per day	\(90\%\) success rate over 3 days [5, 78]
\(\rho\)	Per adult female oviposition rate	16 per day	[79,80,81]
m	Larval maturation rate	0.1 (0.05, 0.17)	[82]
\(\mu _A\)	Adult mosquito death rate	\(\ln \frac{10}{9}\) per day	[73, 76, 77, 83, 84], chosen to be conservative
\(\mu _L\)	Density-independent larval death rate	0.03 per day	[85]
\(\beta\)	Strength of density dependence	0.9	Varies from \(\beta <1\) for contest to \(\beta >1\) for scramble
\(\nu\)	Scale of larval density-dependence	Eq. (4)	Ensures \(A^* = k^* N\)
\(\theta _1\)	Cost per infected individual	\(11.43 \gamma\) \((3.03 \gamma , 37.12 \gamma )\) $ per day	Mean (min, max) from [61]
\(\theta _2\)	Cost of artemisinin therapy	\(\frac{4.61}{3}\) \((\frac{3.96}{3}, \frac{5.57}{3})\) $ per day	Mean (min, max) from [5] assuming 3 day treatment
\(\theta _3 \times 10^4\)	Cost per \(10^4\) insects released	9.11 (1.93, 25.36) $ per day	Mean (min, max) from [43, 86,87,88,89, 89, 90]
\(\psi\)	Future discounting factor	0.1/365 per day	Variable