## 3 Data, Modelling Methods and Analysis Tools
### Agent Model for Malarial Spreading  
To combine results from empirical data with simulations from the agent model introduced and developed in previous works [3; 4], we conduct a series of simulations at different levels of disease transmission efficiency. Human-to-mosquito (H-to-M) transmission was defined in terms of the fraction of human disease days with the presence of gametocytemia in blood circulation, henceforth represented as \(w_{h}\). Six different scenarios were considered, corresponding to a wide range of different levels of positive gametocytemia duration and disease transmission efficiency, specifically, 110 days of positive gametocytemia during 150 days of expected disease duration (i.e., \(w_{h}=110/150=0.733\)), 90 days (\(w_{h}=0.600\)), 75 days (\(w_{h}=0.500\)), 70 days (\(w_{h}=0.467\)), 68 days (\(w_{h}=0.453\)), and 63 days (\(w_{h}=0.420\)). For the simulations, we consider a system of \(N_{m}=4000\) mosquitoes and \(N_{h}=2000\) human individuals, both including healthy and infected individuals. We have modeled the number of mosquitoes as a small but effective fraction of the overall mosquito mass that randomly feeds on a human individual, twice daily on average. The simulation time lasts 30 years while evaluating each human individual in terms of disease duration and human-to-mosquito transmission. The algorithm keeps track of several attributes for each agent, whether human or mosquito, at a particular age, such as the time spent since the first day of infection, and the individual immunity status. Beyond 5 years of persistent human reinfections, the human host will develop partial protective immunity at the maximum possible level, while losing it after 2 years without infection. The computational cycle includes a realistic mosquito daily mortality routine. Dead mosquitoes are to be replaced by uninfected mosquitoes. Human disease duration reflects realistic human recovery from malaria. Human-to-mosquito transmission efficiency (\(w_{h}\)) is also stochastically defined and directly dependent on the number of days with positive gametocytemia. Upon updating the number of healthy humans individuals and mosquitoes, the algorithm generates one episode of mosquito feeding in a human individual, with the possibility of protection from long lasting insecticide-impregnated nets (LLIN), insecticide-impregnated nets (ITN) or \begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multirow{2}{*}{**Empirical Series**} & \multirow{2}{*}{**Year**} & \multicolumn{1}{c}{**I 36 Months**} & \multicolumn{1}{c}{**H 36 Months**} & \multicolumn{1}{c}{**S 36 Months**} & \multicolumn{1}{c}{**Duration**} \\  & & **(I36)** & **(I36)** & **(I36)** & **(I36)** & **(I36)** & **Months** \\ \hline [PERSON] [22] & 2014 & 0.208 \(\pm\) 0.0495 & 0.7766 \(\pm\) 0.1428 & 5.138 \(\pm\) 0.0064 & 132 \\ \hline [PERSON] [21] & 2017 & 7.091 \(\pm\) 2.808 & 1.014 \(\pm\) 0.1425 & 4.792 \(\pm\) 0.1717 & 72 \\ \hline [PERSON] [23] & 2016 & 11.63 \(\pm\) 1.355 & 1.077 \(\pm\) 0.0925 & 5.161 \(\pm\) 0.0036 & 120 \\ \hline [PERSON] [16] & 2015 & 12.44 \(\pm\) 0.1318 & 0.9229 \(\pm\) 0.0570 & 5.121 \(\pm\) 0.0026 & 60 \\ \hline [PERSON] [25] & 2012 & 24.54 \(\pm\) 4.312 & 0.7326 \(\pm\) 0.0850 & 5.065 \(\pm\) 0.0206 & 72 \\ \hline [PERSON] [26] & 2017 & 58.76 \(\pm\) 1.112 & 0.8254 \(\pm\) 0.1236 & 5.160 \(\pm\) 0.0027 & 71 \\ \hline [PERSON] [24] & 2007 & 101.0 \(\pm\) 28.20 & 0.9367 \(\pm\) 0.0993 & 4.710 \(\pm\) 0.1733 & 84 \\ \hline [PERSON] [27] & 2008 & 203.4 \(\pm\) 120.2 & 1.018 \(\pm\) 0.1568 & 4.881 \(\pm\) 0.2774 & 96 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The empirical values of average malaria incidence \(I\) (malaria cases per 100 inhabitants, per year), the Hurst exponent \(H\) and Shannon entropy \(S\), concerning a 36-month time frame. Errord indicate standard deviations from the series by using moving windows of 36 months. indoor residual spraying (IRS).