Integer Linear Programming adalah sebuah model matematis yang memungkinkan hasil penyelesaian kasus pada Pemrograman Linier berupa bilangan bulat. . Masalah integer linear programming termasuk salah satu bagian riset operasi yang sangat penting karena dalam kehidupan sehari-hari, ada banyak permasalah pemrograman linear yang mengharuskan solusinya integer. Ada beberapa metode untuk menyelesaikan persoalan Integer Programming, tapi yang akan dibahas pada penelitian ini adalah Metode Branch and Bound dan Metode Gomory Cut. Tujuan dari penelitian ini adalah untuk menentukan solusi masalah Integer Linear Programming dan membandingkan hasil yang diperoleh dari Metode Branch and Bound dengan Metode Gomory Cut. Penelitian ini adalah penelitian kepustakaan yang menggunakan berbagai literatur-literatur yang berkaitan dengan topik yang akan diteliti. Hasil penelitian ini menunjukkan solusi yang diperoleh dari metode Branch and Bound samadengan metode Gomory Cut. Dalam pemecahannya metode Branch and Bound memerlukan banyak iterasi simpleks dibanding metode Gomory Cut.Kata kunci: Integer Linear Programming, Metode Branch Bound, Metode Gomory Cut

Schistosomiasis is a parasitic disease caused by the schistosoma worm. A snail can act as the intermediate host for the parasite. Snail-population control is considered to be an effective way to control schistosomiasis spread. In this paper, we discuss the schistosomiasis model incorporating a snail predator as a biological control agent. We prove that the solutions of the model are non-negative and bounded. The existence condition of equilibrium points is investigated. We determine the basic reproduction number when the predator goes to extinction and when the predator survives. The local stability condition of disease-free equilibrium point is proved using linearization, and the Lienard–Chipart and Routh–Hurwitz criteria. We use center-manifold theory to prove the local stability condition of the endemic equilibrium points. Furthermore, we constructed a Lyapunov function to investigate the global stability condition of the disease-free equilibrium points. To support the analytical results, we presented some numerical simulation results. Our findings suggest that a snail predator as a biological control agent can reduce schistosomiasis prevalence. Moreover, the snail-predator birth rate plays an essential role in controlling schistosomiasis spread.

Foot and Mouth Disease (FMD) is a highly contagious disease that can infect all cloven hoofed animals. FMD is one of the most important infectious viral diseases in the world. This disease is responsible for international losses in livestock production and trade. In this article, we formulate a mathematical model for the spread of FMD in goat farms that considers early quarantine, vaccination, and disinfection interventions. The model constructed is expressed as a system of ordinary differential equations consisting of eight state variables. We determine the basic reproduction number using the next-generation matrix method. Our numerical simulation results show that vaccination has a very crucial role in controlling the spread of FMD and reducing the basic reproduction number. In addition, quarantine interventions for latent and infectious goats are also effective in controlling the spread of FMD. The basic reproduction number can also be suppressed by disinfection and quarantine interventions. Therefore, we recommend implementing routine vaccination, screening and disinfection programs. In addition, farmer should be given education so that they have the ability to identify goats exposed to FMDV so that quarantine can be carried out early.

Armed Criminal group is one of the problems faced by many countries in the world. Awful behaviour of armed criminal group members can affect a large amount of people. In this paper, we construct a deterministic mathematical model that takes into account persuasive and repressive intervention. We consider crime as a social epidemic. We determine the armed criminal group free equilibrium point and the armed criminal group persistence equilibrium point together with their existence condition. The next generation matrix is used to obtain the basic reproduction number. The local stability conditions of equilibrium points are proved using linearization. We show that the armed criminal group free equilibrium point is globally asymptotically stable under certain condition. Numerical simulations are performed to support our deductive study.

In this work, a deterministic mathematical model of schistosomiasis transmission dynamics is discussed. In rural areas, many people work as a cattle farmer. Cattle farmers in endemic areas are very susceptible to schistosoma worm infection. To study the dynamics of schistosomiasis spread in traditional cattle farmer communities, we develop a mathematical model by considering human, cattle, and snail population as well as parasite density in environment. The model is expressed as a system of first order differential equations. Firstly, we verify the non-negativity and boundedness of the solutions of the model. After determining the equilibrium points of the system, we determine the basic reproduction number. Linearization and Routh Hurwitz condition are used to analyze the local stability condition of the disease free equilibrium point. Center manifold theory is used to study the local stability condition of the endemic equilibrium point. We prove global stability condition of the disease free equilibrium point by formulating suitable Lyapunov function and using LaSalle invariance principle. Several numerical simulations are presented. Our results show that the farmer should keep the cattle, water, and food clean. In addition, the farmer should use molluscicide in their farm area and give schistosomiasis drug to the cattle, regularly.