This article explains a nonlinear mathematical model of forestry biomass depletion due to human population, population pressure and industrialization. The model also considers crowding by industrialization. Analysis of model shows that equilibrium level the biomass density of forestry resources decreases as the equilibrium level in density of human population, population pressure and industrialization increase. It is found that if the crowding by industrialization increases, then biomass density of forestry resources decreases. Therefore, it is necessary control industrialization to protect the forestry resources stability.

In this article, the homotopy analysis method is applied to obtain approximate analytical solution for a single species population model with viral infection in polluted environment. The resulting solutions are compared with the numerical method. The comparison reveals that our approximate solutions are in very good agreement with the solutions by numerical method. Moreover, The result show that the homotopy analysis method is very e¤ective and simple for solving the nonlinear ordinary di¤erential equation systems.

Improving services through goods pickups and deliveries to expand the market is currently being carried out by many companies. This effort needs another step of optimization to avoid losses due to additional resources, such as time, which must be held by the company. In the case of simultaneous goods pickups and deliveries using a vehicle with single transport access, the policy of arranging goods in the vehicle can affect the length of time for service. Single transport access causes goods that want to be unloaded obstructed by the other goods, thus requires additional time for handling. In this paper, the problem of a vehicle’s route and handling time in picking and delivering goods with time windows is modeled as the Traveling Salesman Problem. The objective function of this problem is to minimize the total travel time and handling time during the picking and delivering goods. The model is implemented in the case of bicycle pickup and delivery services involving 15 bicycle shops. The capacity of the vehicle is 15 units of bicycle. In this case, a solution consisting the pickup and delivery route and optimal goods order is obtained with an objective function value of 334 minutes.

No abstract

In this paper, we study an SVEIR disease model of tuberculosis transmission dynamics in which the infected population is divided into two groups, namely infectious infected and noninfectious infected population. The equilibrium points and the basic reproduction number R 0 are determined. The stability analysis of the model was conducted by considering the basic reproduction number R 0. We show that if R 0 < 1, then the disease-free equilibrium is locally asymptotically stable. If R 0 > 1, then a unique endemic equilibrium is locally asymptotically stable.