## 3 System Model
### AO-PF Fusion Algorithm  
#### 3.6.1 AO Algorithm  
The artemisinin optimization (AO) algorithm [38] is a novel metaheuristic algorithm inspired by the artemisinin treatment process for malaria. It simulates the diffusion, concentration changes, and elimination of artemisinin in the human body. The algorithm comprises four main stages: initialization, comprehensive elimination, local elimination, and post-consolidation.  
First, the AO algorithm performs initialization, simulating the injection of artemisinin into the human body. The drug's microparticles are likened to the search agents in the algorithm. The collection of these search agents constitutes the solution set of the algorithm. \(X\) represents the entire drug population after initialization, where \(N\) denotes the number of search agents and \(D\) denotes the multi-dimensional components within each search agent, indicating the dimension of the matrix.  
\[X_{N,D}=B+R\times(T-B)=\begin{bmatrix}x_{1,1}&x_{1,2}&\cdots&x_{1,D}\\ x_{2,1}&x_{2,2}&\cdots&x_{2,D}\\ \vdots&\vdots&\ddots&\vdots\\ x_{N,1}&x_{N,2}&\cdots&x_{N,D}\end{bmatrix} \tag{19}\]  
where \(T\) and \(B\) represent the boundaries of the solution space, and \(R\) represents a random number between 0 and 1.  
Next is the comprehensive elimination stage. The strategy for this stage is shown in the following equation:  
\[\begin{cases}x_{i,j}^{t+1}=x_{i,j}^{t}+c\times x_{i,j}^{t}\times(-1)^{t},rand <0.5\\ x_{i,j}^{t+1}=x_{i,j}^{t}+c\times best_{j}^{t}\times(-1)^{t},rand>0.5^{t},r1<K \end{cases} \tag{20}\]  
where \(K=1-\frac{f^{1/6}}{Maxf^{1/6}}\) is the probability coefficient, \(c=1\times e^{-(4\times\frac{f}{Maxf})}\) represents the attenuation index of artemisinin in the human body, \(f\) and \(maxf\) represent the current and maximum number of iterations, and the variable \(r1\) is a random number uniformly distributed in the range \([0,1]\).  
The next phase is the local elimination stage, aimed at eliminating residual malaria parasites.  
\[x_{i}^{t+1}=x_{b_{3}}^{t}+d\times\left(x_{b_{1}}^{t}-x_{b_{2}}^{t}\right),if \leavevmode\
obreak\ rand<Fit_{norm}(i) \tag{21}\]\[Fit_{norm}(i)=\frac{fit(i)-\min(fit)}{\max(fit)-\min(fit)} \tag{22}\]  
\[b_{1},b_{2},b_{3}\sim U(1,N),b_{1}\
eq b_{2}\
eq b_{3} \tag{23}\]  
where \(Fit_{norm}(i)\) represents the normalized fitness value, \(d\) denotes a random value between 0.1 and 0.6, and \(b_{1},b_{2},b_{3}\) represent the indexes of three randomly selected search agents, which are uniformly distributed.  
The final phase is post-consolidation. Consolidation treatment of dormant malaria parasites is needed. The equation is as follows. If rand is less than 0.05, the search agent's position remains unchanged; if rand is less than 0.2, the search agent's position is updated to the corresponding dimension value of the current optimal solution.  
\[\left\{\begin{aligned} & x_{i,j}^{t+1}=x_{i,j}^{t},if\;rand<0.05\\ & x_{i,j}^{t+1}=best_{i,j},if\;rand<0.2\end{aligned}\right. \tag{24}\]  
where \(best_{i,j}\) represents the value of the best-performing individual in the \(j\)-th dimension within the current population, found in the \(i\)-th search agent, and rand is a random number uniformly distributed in the interval [0, 1].  
AO introduces a global search mechanism, enhancing the diversity of particles. By optimizing particle positions using AO, the algorithm ensures that particles explore a broader state space, reducing the risk of particle impoverishment. AO adjusts particle weights based on their fitness, which is determined by the match between particle states and observed data. This helps maintain a set of particles that more accurately represent the true state.