D. Aldila

An optimal control problem arising from a dengue disease transmission model

An optimal control problem for a host-vector Dengue transmission model is discussed here. In the model, treatments with mosquito repellent are given to adults and children and those who undergo treatment are classified in treated compartments. With this classification, the model consists of 11 dynamic equations. The basic reproductive ratio that represents the epidemic indicator is obtained from the largest eigenvalue of the next generation matrix. The optimal control problem is designed with four control parameters, namely the treatment rates for children and adult compartments, and the drop-out rates from both compartments. The cost functional accounts for the total number of the infected persons, the cost of the treatment, and the cost related to reducing the drop-out rates. Numerical results for the optimal controls and the related dynamics are shown for the case of epidemic prevention and outbreak reduction strategies.

Optimal Control Problem of Treatment for Obesity in a Closed Population

Variety of intervention programs for controlling the obesity epidemic has been done worldwide. However, it is still not yet available a scientific tool to measure the effectiveness of those programs. This is due to the difficulty in parameterizing the human interaction and transition process of obesity. A dynamical model for simulating the interaction between healthy people, overweight people, and obese people in a randomly mixed population is discussed in here. Two scenarios of intervention programs were implemented in the model, dietary program for overweight people with healthy life campaign and treatment program for obese people. Assuming all control rates are constant, disease free equilibrium point, endemic equilibrium point, and basic reproductive ratio () as the epidemic indicator were shown analytically. We find that the disease free equilibrium point is locally asymptotical stable if and only if . From sensitivity analysis of , we obtain that larger rate of dietary program and treatment program will reduce significantly. With control rates are continuous in time, an optimal control approach was applied into the model to find the best way to minimize the number of overweight and obese people. Some numerical analysis and simulations for optimal control of the intervention were shown to support the analytical results.

Mathematical model in controlling dengue transmission with sterile mosquito strategies

In this article, we propose a mathematical model for controlling dengue disease transmission with sterile mosquito techniques (SIT). Sterile male introduced from lab in to habitat to compete with wild male mosquito for mating with female mosquito. Our aim is to displace gradually the natural mosquito from the habitat. Mathematical model analysis for steady states and the basic reproductive ratio are performed analytically. Numerical simulation are shown in some different scenarios. We find that SIT intervention is potential to controlling dengue spread among humans population

Mathematical model of temephos resistance in Aedes aegypti mosquito population

Aedes aegypti is the main vector of dengue disease in many tropical and sub-tropical countries. Dengue became major public concern in these countries due to the unavailability of vaccine or drugs for dengue disease in the market. Hence, the only way to control the spread of DF and DHF is by controlling the vectors carrying the disease, for instance with fumigation, temephos or genetic manipulation. Many previous studies conclude that Aedes aegypti may develop resistance to many kind of insecticide, including temephos. Mathematical model for transmission of temephos resistance in Aedes aegypti population is discussed in this paper. Nontrivial equilibrium point of the system and the corresponding existence are shown analytically. The model analysis have shown epidemiological trends condition that permits the coexistence of nontrivial equilibrium is given analytically. Numerical results are given to show parameter sensitivity and some cases of worsening effect values for illustrating possible conditions in t...

A survey of basic reproductive ratios in vector-borne disease transmission modeling

Vector-borne diseases are commonly known in tropical and subtropical countries. These diseases have contributed to more than 10% of world infectious disease cases. Among the vectors responsible for transmitting the diseases are mosquitoes, ticks, fleas, flies, bugs and worms. Several of the diseases are known to contribute to the increasing threat to human health such as malaria, dengue, filariasis, chikungunya, west nile fever, yellow fever, encephalistis, and anthrax. It is necessary to understand the real process of infection, factors which contribute to the complication of the transmission in order to come up with a good and sound mathematical model. Although it is not easy to simulate the real transmission process of the infection, we could say that almost all models have been developed from the already long known Host-Vector model. It constitutes the main transmission processes i.e. birth, death, infection and recovery. From this simple model, the basic concepts of Disease Free and Endemic Equilibri...

Mathematical model for the spread of extreme ideology

Mathematical model to understand the spread of extreme ideology in a closed population will be discussed in this paper. Human population divided into five sub-population, i.e virgin sub-population, semi fanatic sub-population, fanatic sub-population, aware sub-population and recovered sub-population. Intervention to rehabilitate first three sub-population (virgin, semi fanatic and fanatic) included in this model as an effort by the government to control the spread of the ideology. Equilibrium points and their threshold conditions are shown analytically. Some numerical simulation are given to support the analytic results. It is shown that isolate fanatic people and educate them is a better solution rather than to give an education about the danger of the extreme ideology to source population.

On the analysis of effectiveness in mass application of mosquito repellent for dengue disease prevention

Dengue disease has been known as one of dangerous vector-borne diseases and become serious threat in many tropical countries. With no vaccine and antiviral available until nowadays, and frequent appearance of extraordinary dengue outbreaks, many governments are forced to declare national problem for dengue. At this moment, the only method available to prevent dengue disease transmission is to combat the disease-carrying mosquitoes as well as to reduce the contact between human and mosquitoes. The fast growing dengue transmission in many countries in recent years indicates that the mosquito control programs are far from successful. The use of mosquito repellent is one possible instrument which could be used as an effective mass treatment to prevent the dengue outbreak during endemic period. Here in this paper a Susceptible-Infectious-Recovered (S-I-R) dengue transmission model with repellent mass treatment is being applied to portions of children and adult compartments. Analysis of the basic reproductive r...

Mathematical model for transmission of tuberculosis in badger population with vaccination

Badger was first time identified as a carrier of Bovine tuberculosis disease in England since 30 years ago. Bovine tuberculosis can be transmitted to another species through the faces, saliva, and breath. The control of tuberculosis in the badger is necessary to reduce the spread of the disease to other species. Many actions have been taken by the government to tackle the disease such as culling badgers with cyanide gas, but this way destroys the natural balance and disrupts the badger population. An alternative way to eliminate tuberculosis within badger population is by vaccination. Here in this paper a model for transmission of badger tuberculosis with vaccination is discussed. The existence of the endemic equilibrium, the stability and the basic reproduction ratio are shown analytically. Numerical simulations show that with proper vaccination level, the basic reproduction ratio could be reduced significantly. Sensitivity analysis for variation of parameters are shown numerically.

On the analysis of parasite effect for Aedes aegypti and Aedes albopictus population

It has been reported in some countries that the population of Aedes aegypti has been significantly reduced by the invasion of Aedes albopictus. There has been a hypothesis explaining this phenomenon of which investigated the influence of parasites pathogenesis to the competition between these two mosquito species in the fields. Ascogregarina taiwanensis and Ascogregarina culicis are known as parasites that infect Aedes albopictus and Aedes aegypti, respectively. Several studies have concluded that Ascogregarina taiwanensis caused high fatality for Aedes aegypti larvae, but Ascogregarina culicis was not pathogenic to Aedes albopictus larvae. Therefore, Ascogregarina taiwanensis may contribute to reduce the number of populations Aedes aegypti in the fields. Inspired by these facts, a mathematical model depicting interaction between parasites and mosquitoes is constructed in this paper. In this model are included six dynamic mosquito compartments, i.e. egg, larvae, infected larvae, adult, infected adult and one dynamic compartment for parasite. Derivation of the existence criteria and the stability analysis of parasite-free equilibrium as well as the basic offspring for the model are presented. Numerical simulations for sensitivity analysis indicating the invasive species for variation parameters are shown.

Optimal control of diarrhea transmission in a flood evacuation zone

Evacuation of residents and diarrhea disease outbreak in evacuation zone have become serious problem that frequently happened during flood periods. Limited clean water supply and infrastructure in evacuation zone contribute to a critical spread of diarrhea. Transmission of diarrhea disease can be reduced by controlling clean water supply and treating diarrhea patients properly. These treatments require significant amount of budget, which may not be fulfilled in the fields. In his paper, transmission of diarrhea disease in evacuation zone using SIRS model is presented as control optimum problem with clean water supply and rate of treated patients as input controls. Existence and stability of equilibrium points and sensitivity analysis are investigated analytically for constant input controls. Optimum clean water supply and rate of treatment are found using optimum control technique. Optimal results for transmission of diarrhea and the corresponding controls during the period of observation are simulated nu...