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Table 2 Malaria transmission parameter values for the baseline, untreated case (corresponding to the subscript “u”) and treatment cases (corresponding to the subscript “t”)

From: Multi-year optimization of malaria intervention: a mathematical model

Symbol Description Baseline value
Treatment value
\(a_u\), \(a_t\) Bites per mosquito per human per day 0.25 [33] \(a_u(1-\beta )\) [15]     
\(b_u\), \(b_t\) Transmission efficacy from infected mosquito to susceptible, untreated human 0.022 [33]    0.0047   0.005
\(\beta\) Proportion of bites that would occur while sleeping   0.8 [15]     
c Transmission efficacy from infected human to mosquito 0.36 [33]      
\(\delta\) Daily birth rate and death rate assuming constant population \(4.7895*10^{-5}\) [34]      
\(\gamma _u\), \(\gamma _t\) Recovery rate in humans \(\frac{1}{180}\) [35]     \(\frac{1}{10}\) \(\frac{1}{5.5}\)
\(m_u\), \(m_t\) Mosquitoes per human 20 [13] \(m_u(1-\beta \chi _{LLIN})\) \(m_{u,IRS}=m_u(1-q\chi _{IRS_u})\)
\(m_{t}=m_u(1-\chi _{IRS_t})\) [38]
\(\mu\) Mosquito mortality rate 0.095 [35, 36]      
\(\omega\) Duration of immunity without reinfection 274 days [37]      
q Treatment coverage 0.2, 0.4 or 0.6      
\(\tau\) Incubation period in mosquito 10 days [36]      
x Fraction of the population 0.146 [34]      
  0–4 years of age       
\(\chi _{LLIN}\) Probability of mosquito mortality when exposed to a treated net   0.8 [14]     
\(\chi _{IRS_t}\) Percent reduction in mosquito density in a house treated with IRS    0.95 [38]    
\(\chi _{IRS_u}\) Percent reduction in mosquito density in an untreated house when all nearby houses are treated with IRS    0.5 [38]    
  1. In the baseline value column, an empty space means that the parameter does not apply to the baseline, untreated case. In the treatment value columns, an empty space means that the parameter is unchanged by that particular intervention