Table 1.
Descriptions, baseline values and ranges of values of parameters for the malaria model (2.4). Human recruitments consist of new human births and immigrants. Using estimated birth rates from Central Intelligence Agency (CIA) (2014a) for the 10 sub-Saharan African countries that accounted for about 87% of residents in hyperendemic or holoendemic malaria regions in 2010 Noor et al. (2014), we obtain a birth rate of approximately 38 births per thousand per year. We assume an approximate human immigration rate of 18 humans per year, which is within the range in Chitnis et al. (2008). Also, we assume that 40% of infectious humans recover without acquiring immunity and that the minimum biting rate is 1/102 bites on humans per mosquito per day. Assuming a non-zero minimum mosquito-biting rate is reasonable, since, due to inefficient usage, decay in ITN-efficacy, possible human activities out of ITNs at night, etc., ITN protection against mosquito-bites might not be 100% efficient.
| Parameter | Description and dimension | Baseline value | Range | Reference |
|---|---|---|---|---|
| Λh | Human recruitment rate (Humans × day−1) | 103/(55 × 365) | [103/72, 103/35] × 1/365 | Chitnis et al. (2008), Central Intelligence Agency (CIA) (2014a) |
| Λv | Mosquito recruitment rate (Mosquitoes × day−1) | 104/14 | [104/21, 104/14] | Teboh-Ewungkem (2009) |
| μh | Human natural death rate (Day−1) | 1/(55 × 365) | [1/72, 1/35] × 1/365 | Central Intelligence Agency (CIA) (2014b) |
| μv0 | Mosquito natural death rate (Day−1) | 1/14 | [1/21, 1/14] | Davidson and Draper (1953), Giles and Warrel (2002) |
| μ̃v | ITN-induced mosquito death rate(Day−1) | 1/14 | [1/21, 5/10] | Lines et al. (1987) |
| δh | Human disease-induced death rate (Day−1) | 32.9/(365 × 103) | [0, 41/105] | Chitnis et al. (2008) |
| νh | Rate at which exposed humans become infectious (Day−1) | 1/14 | [67/103, 2/10] | Molineaux and Gramiccia (1980), Mehlhorn and Armstrong (2001), Chitnis et al. (2008) |
| νv | Rate at which exposed mosquitoes become infectious (Day−1) | 1/10 | [29/103, 33/102] | Macdonald et al. (1957), Chitnis et al. (2008) |
| σ̃h | Rate at which infectious humans acquire immunity (Day−1) | 1/285 | [14/104, 17/103] | Molineaux and Gramiccia (1980), Chitnis et al. (2008) |
| α | Proportion of infectious humans who recover without acquiring immunity (Dimensionless) | 4/10 | [0, 1] | |
| γ̃h | Rate at which infectious humans recover without acquiring immunity (Day−1) | 1/4 | [1/180, 1/4] | Filipe et al. (2007) |
| ρh | Rate at which immune humans lose immunity (Day−1) | 1/(5 × 365) | [55/106, 11/103] | Chitnis et al. (2008) |
| βmin | Minimum mosquito biting rate (Day−1) | 1/102 | [0, 1/10] | |
| βmax | Maximum mosquito biting rate (Day−1) | 5/10, 1 | [1/10, 1] | Molineaux et al. (1979), Gupta et al. (1994), Chitnis et al. (2008) |
| b0 | Initial personal protection or ITN coverage (Dimensionless) | 53/100 | [0, 1] | World Health Organization (WHO) (2012), Malaria Communities Program (2014) |
| T | Useful life of insecticide-treated nets (ITNs) (Day) | 3 × 365 | [180, 3 × 365] | WHO (2007), WHO (2011), Pulkki-Brännström et al. (2012) |
| pvh | Disease transmission probability from infectious mosquitoes to susceptible humans (Dimensionless) | 22/103 | [1/102, 27/102] | Davidson and Draper (1953), Krafsur and Armstrong (1978), Nedelman (1985) |
| phv | Disease transmission probability from infectious humans to susceptible mosquitoes (Dimensionless) | 48/102 | [72/103, 64/102] | Boyd (1949), Smalley and Sinden (1977), Nedelman (1984) |
| θphv | Disease transmission probability from immune humans to susceptible mosquitoes (Dimensionless) | 48/103 | [72/104, 64/102] | Boyd (1949), Smalley and Sinden (1977), Nedelman (1984) |