M. A. Masud

Optimal Implementation of Intervention to Control the Self-harm Epidemic.

Objectives Deliberate self-harm (DSH) of a young person has been a matter of growing concern to parents and policymakers. Prevention and early eradication are the main interventional techniques among which prevention through reducing peer pressure has a major role in reducing the DSH epidemic. Our aim is to develop an optimal control strategy for minimizing the DSH epidemic and to assess the efficacy of the controls. Methods We considered a deterministic compartmental model of the DSH epidemic and two interventional techniques as the control measures. Pontryagins Maximum Principle was used to mathematically derive the optimal controls. We also simulated the model using the forward-backward sweep method. Results Simulation results showed that the controls needed to be used simultaneously to reduce DSH successfully. An optimal control strategy should be adopted, depending on implementation costs for the controls. Conclusion The long-term success of the optimum control depends on the implementation cost. If the cost is very high, the control could be used for a short term, even though it fails in the long run. The control strategy, most importantly, should be implemented as early as possible to attack a comparatively fewer number of addicted individuals.

Analysis of a vector-bias effect in the spread of malaria between two different incidence areas

In 2005, Lacroix et al. demonstrated that infected humans are more attractive to mosquitoes, a phenomenon known as the vector-bias effect. The aim of this study was to determine how a vector-bias effect affects the changes in the dynamics of malaria transmission, and the changes in control strategies and cost-effectiveness for optimal control considering the regional characteristics or force of infections for different transmission rates. We used a vector-bias mathematical model and considered two different incidence areas: a high transmission area and a low transmission area. Our results showed that the dynamics in the two areas differed; as bias exists and the strategy for optimal control could be changed in the different areas. Thus, this work may give that considering the vector-bias effect in different areas facilitates prediction of the future dynamics and make decisions for establishing controls. We also mention the evolution of malaria parasites in this study.

Optimal Implementation of Intervention Strategies for Elderly People with Ludomania

Objectives Now-a-days gambling is growing especially fast among older adults. To control the gratuitous growth of gambling, well-analyzed scientific strategies are necessary. We tried to analyze the adequacy of the health of society mathematically through immediate treatment of patients with early prevention. Methods The model from Lee and Do was modified and control parameters were introduced. Pontryagins Maximum Principle was used to obtain an optimal control strategy. Results Optimal control can be achieved through simultaneous use of the control parameters, though it varies from society to society. The control corresponding to prevention needed to be implemented in full almost all the time for all types of societies. In the case of the other two controls, the scenario was greatly affected depending on the types of societies. Conclusion Prevention and treatment for elderly people with ludomania are the main intervention strategies. We found that optimal timely implementation of the intervention strategies was more effective. The optimal control strategy varied with the initial number of gamblers. However, three intervention strategies were considered, among which, preventing people from engaging in all types of gambling proved to be the most crucial.

Optimal control problems of mosquito-borne disease subject to changes in feeding behavior of Aedes mosquitoes

Dengue viruses (DENV) are transmitted to humans by the bite of Aedes mosquitoes. It is known that dengue virus infection in Aedes aegypti female mosquitoes makes a change in the feeding behavior of the infected mosquitoes. In this study, using the forces of infection, we incorporated the effect of changes in the feeding behavior of mosquitoes into the standard vector-borne SIR-SI model. It has been proved that both a single-strain model and a two-strain model exhibit forward bifurcations. Moreover, optimal implementations of control with specific prevention measures for dengue transmission are analyzed. As a result we found that more implementation of controls on the secondary infection of humans should be considered for the behavioral changes in feeding of the infected mosquitoes.