## 2 Methods, Model, and Analysis Tools
### Human-to-Mosquito Transmission and Drug Administration in a Heterogeneity Setting
At this point, we clarify a few aspects to address the limitations of our approach and better establish the context of this agent-based simulation scenario. In order to include the effect of ivermectinin our model, we needed to use a simplified computational procedure replicating the consequences of mosquito feeding on human individuals under ivermectin treatment. Although this procedure may be considered overly simplistic, it is, none the less, computationally efficient, being based on a simple Bernoulli process in order to decide the fate of the mosquito after feeding on a human individual under ivermectin. In this way, one does not take into account aspects that could be addressed in the clinical context, namely ivermectin pharmacokinetics and pharmacodynamics [23]. Our validation procedure focuses on comparing mosquito survival data from our model simulation with data from empirical mosquito survival data, such as presented in [22]. We did not include any other pharmacokinetic concept in our computational algorithm, as we considered the assumption from published data, that 50% of mosquitoes would die within four days after feeding on a human host under ivermectin treatment, valid. In our computational algorithm, we pretend to simulate ivermectin toxicity with a simpler procedure, ignoring other more complex pharmacokinetic concepts. The impact of ivermectin in inducing mild mosquito mortality in the time spent during disease incubation is, most likely, the critical factor in reducing disease transmission with ivermectin treatment, as the effect of ivermectin in global mosquito density is mainly residual. Our validation procedure was essentially based on determining the mosquito survival distribution curves from our model and whether they would be compatible with the expected results obtained from our pharmacokinetic assumptions for the mosquito survival distribution curves, when compared to empirical data, such as presented in [22]. Predictive Rates for Assessing the Strength of Malaria Transmission and the Annual Entomological Inoculation  
Field malaria transmission is difficult to monitor, requiring various methods to measure different aspects of disease transmission [41]. Here, we consider three metrics to monitor the intensity of malaria transmission: (a) malaria incidence (\(MI\)), (b) parasite rate (\(X\)) for human individuals, and (c) sporozoite rate (\(Z\)) for mosquitoes. Malaria incidence is defined as the confirmed malaria cases per person per unit of time and, in particular, as the annual number of confirmed malaria cases per 100 inhabitants at risk. The parasite rate \(X\) is given by the fraction of infected humans and is also known as the prevalence of infection in humans [6; 42]. This rate is obtainable from the slide positivity rate (SPR), which is defined as the number of microscopy-confirmed malaria tests per 100 suspected cases examined [43]. SPR is useful in establishing temporal trends in malaria and simple to implement at peripheral health facilities. It only considers laboratory confirmed cases of malaria and may also be derived from rapid diagnostic testing (RDT-PR) [44]. SPR has been associated with malaria incidence and identified as a strong predictor of malaria transmission in Yunnan province, China [45]. The sporozoite rate \(Z\) represents the fraction of infected mosquitoes [42; 46]. Although these two indices, \(Z\) and \(X\), are commonly used separately in malaria research [42], we combined their behavior with respect to heterogeneity, introducing a \"global infection rate\" \(G\) parameter, which is given by the product of both rates:  
\[G\sim ZX\,, \tag{6}\]  
where the pre-factor is introduced in order to have the result in the form of a squared percentage. Related to these predictive rates is the annual entomological inoculation rate (EIR) defined as:  
\[\text{EIR}=365\,m\,a\,Z\,, \tag{7}\]  
where, as stated above, \(m\) is the mosquito density and \(a\) is the human feeding rate.