Malaria is one of the world's most serious health problems because of the increasing number of cases every year. First, we discuss a deterministic model of epidemic SIR-SI spread of malaria with the intervention of bed nets and fumigation. We found that the malaria-free equilibrium is locally asymptotically stable (LAS) when R 0 < 1 and unstable otherwise. A malaria endemic equilibrium exists and is LAS when R 0 > 1. Sensitivity analysis of R 0 shows that the use of bed nets and fumigation can reduce R 0 . We modify the previous model into a stochastic differential equation model to understand the effect of random environmental factors on the spread of malaria.Numerical simulations show that when R 0 > 1, a greater value of noise intensity σ generates a solution that is different from a deterministic solution; when R 0 < 1, regardless of the σ value, the solution approaches a deterministic solution. Then the deterministic model was modified into an optimal control model to determine the best strategy in controlling the spread of malaria by using fumigation as the control variable. Numerical simulations show that periodic fumigations cost less than constant intervention and can reduce the number of infected humans. Priority is given to the endemic prevention strategy rather than to the endemic reduction strategy. For more effective intervention, the value of R 0 should receive close attention. A potentially endemic (R 0 > 1) environment requires more frequent fumigation than an environment that is not potentially endemic (R 0 < 1). A combination of the use of bed nets and fumigation can reduce the number of infected individuals at minimal cost.

No abstract

<abstract><p>A deterministic model which describes measles' dynamic using newborns and adults first and second dose of vaccination and medical treatment is constructed in this paper. Mathematical analysis about existence of equilibrium points, basic reproduction number, and bifurcation analysis conducted to understand qualitative behaviour of the model. For numerical purposes, we estimated the parameters' values of the model using monthly measles data from Jakarta, Indonesia. Optimal control theory was applied to investigate the optimal strategy in handling measles spread. The results show that all controls succeeded in reducing the number of infected individuals. The cost-effective analysis was conducted to determine the best strategy to reduce number of infected individuals with the lowest cost of intervention. Our result indicates that the use of the first dose measles vaccine with medical treatment is the most optimal strategy to control measles transmission.</p></abstract>

Multiple Traveling Salesman Problem (MTSP) is a generalization of the Traveling Salesman Problem (TSP). MTSP is an optimization problem to find the minimum total distance of m salesmen tours to visit several cities in which each city is only visited exactly by one salesman, starting from origin city called depot and return to depot after the tour is completed. In this paper, K-Means and Crossover Ant Colony Optimization (ACO) are used to solve MTSP. The implementation is observed on three datasets from TSPLIB with 2, 3, 4, and 8 salesmen. Analysis of results using K-Means and Crossover ACO will be compared. The effect of selecting a city as depot on the total travel distance of tour will also be analyzed.

<abstract><p>We developed a new mathematical model for yellow fever under three types of intervention strategies: vaccination, hospitalization, and fumigation. Additionally, the side effects of the yellow fever vaccine were also considered in our model. To analyze the best intervention strategies, we constructed our model as an optimal control model. The stability of the equilibrium points and basic reproduction number of the model are presented. Our model indicates that when yellow fever becomes endemic or disappears from the population, it depends on the value of the basic reproduction number, whether it larger or smaller than one. Using the Pontryagin maximum principle, we characterized our optimal control problem. From numerical experiments, we show that the optimal levels of each control must be justified, depending on the strategies chosen to optimally control the spread of yellow fever.</p></abstract>