In this paper we discuss a mathematical model for the transmission of Lymphatic Filariasis diseas... more In this paper we discuss a mathematical model for the transmission of Lymphatic Filariasis disease in Jati Sampurna, West Java Indonesia. The model assumes that acute infected humans are infectious and treatment is given to a certain number of acute infected humans found from screening process. The treated acute individuals are assumed to be remain susceptible to the disease. The model is analyzed and it is found a condition for the existence and stability of the endemic equilibrium. A well known rule of thumb in epidemiological model, that is, the endemic equilibrium exists and stable if the basic reproduction number is greater than one, is shown. Moreover, it is also shown that if the level of screening n is sufficiently large, current medical treatment strategy will be able to reduce the long-term level of incidences. However, in practice it is not realistic and cannot eliminate the disease, in terms of reducing the basic reproduction number. The reproduction number can be reduced by giving additional treatments, such as reducing the biting rate and mosquito's density. This suggests that there should be a combination of treatment to eliminate the disease.
ABSTRACT It has been indicated that a long term application of combined mass drug treatment may c... more ABSTRACT It has been indicated that a long term application of combined mass drug treatment may contribute to the development of drug resistance in lymphatic filariasis. This phenomenon is not well understood due to the complexity of filaria life cycle. In this paper we formulate a mathematical model for the spread of mass drug resistant in a filaria endemic region. The model is represented in a 13-dimensional Host-Vector system. The basic reproductive ratio of the system which is obtained from the next generation matrix, and analysis of stability of both the disease free equilibrium and the coexistence equilibria are shown. Numerical simulation for long term dynamics for possible field conditions is also shown.
In 2000 WHO had issued a Global Program to Eliminate Lymphatic Filariasis by 2020. Lymphatic Fila... more In 2000 WHO had issued a Global Program to Eliminate Lymphatic Filariasis by 2020. Lymphatic Filariasis is an infectious disease that may cause permanent disability to the infected human. This disease is caused by parasitic worms and transmitted by mosquitoes. In the acute cases, the infected persons will undergo swelling in parts of their body. One of the treatment which has been successfully implemented in some countries is the Diethylcarbamazine (DEC) mass treatment. This treatment, which was implemented every ...
ABSTRACT The Blue Mountains Water Skink, Eulamprus leuraensis, is listed as an endangered species... more ABSTRACT The Blue Mountains Water Skink, Eulamprus leuraensis, is listed as an endangered species under the IUCN Red List. This lizard species has a typical characteristic of growth with a low fecundity. It is known that the offspring quality may decline with maternal age of the parents despite they can grow rapidly from neonatal size to adult size within two to three years. It is also believed that low adult survival rates and specialization on rare and fragmented type of habitat are the main cause leading to the endangered status of the lizard. A mathematical model with age structure for Eulamprus leuraensis, taking into account the variation of survival rate in each structure and the declining of offspring quality with respect to maternal age is considered here. Stable coexistence of non-trivial equilibriumis shown. It is also shown that an endangered status is due to combination oflow reproductive output and low rates of adult survival. Further, understanding the age structure within populations can facilitate efective management of the endangered species.
ABSTRACT Aedes aegypti is the main vector of dengue disease in many tropical and sub-tropical cou... more ABSTRACT 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 the field.
In this paper, we discuss a two-age-classes dengue transmission model with vaccination. The reaso... more In this paper, we discuss a two-age-classes dengue transmission model with vaccination. The reason to divide the human population into two age classes is for practical purpose, as vaccination is usually concentrated in one age class. We assume that a constant rate of individuals in the child-class is vaccinated. We analyze a threshold number which is equivalent to the basic reproduction number. If there is an undeliberate vaccination to infectious children, which worsens their condition as the time span of being infectious increases, then paradoxically, vaccination can be counter productive. The paradox, stating that vaccination makes the basic reproduction number even bigger, can occur if the worsening effect is greater than a certain threshold, a function of the human demographic and epidemiological parameters, which is independent of the level of vaccination. However, if the worsening effect is to increase virulence so that one will develop symptoms, then the vaccination is always productive. In both situations, screening should take place before vaccination. In general, the presence of class division has obscured the known rule of thumb for vaccination.
ABSTRACT This paper presents a model of tuberculosis transmission with vaccination by explicitely... more ABSTRACT This paper presents a model of tuberculosis transmission with vaccination by explicitely considering the total number of recovered individuals, either from natural recovery or due to vaccination. In this paper the endemic and nonendemic fixed points, basic reproduction number, and vaccination reproduction number are given. Some results regarding the stability of the fixed points and the relation to the basic reproduction numbers are analysed. At the end of this study, the numerical computation presented and it shows that vaccination is capable to reduce the number of laten and infectious populations.
ABSTRACT In this paper we formulate a model of dengue fever transmission by considering the prese... more ABSTRACT In this paper we formulate a model of dengue fever transmission by considering the presence of asymptomatic and symptomatic compartments. The model takes the form as a system of differential equations representing a host-vector SIR (Susceptible - Infective -Recovered) disease transmission. It is assumed that both host and vector populations are constant. It is also assumed that reinfection of recovered hosts by the disease is possible due to a wanning immunity in human body. We analyze the model to determine the qualitative behavior of the model solution and use the concept of effective basic reproduction number (fraktur Rp) as a control criteria of the disease transmission. The effect of mosquito biting protection (e.g. by using insect repellent) is also considered. We compute the long-term ratio of the asymptomatic and symptomatic classes and show a condition for which the iceberg phenomenon could appear.
In this paper we present a deterministic, discrete-time model for a two-patch predator-prey metap... more In this paper we present a deterministic, discrete-time model for a two-patch predator-prey metapopulation. We study optimal harvesting for the metapopulation using dynamic programming. Some rules are established as generalizations of rules for a single-species metapopulation harvesting theory. We also establish rules to harvest relatively more (or less) vulnerable prey subpopulations and more (or less) efficient predator subpopulations.
In this paper we discuss a mathematical model for the transmission of Lymphatic Filariasis diseas... more In this paper we discuss a mathematical model for the transmission of Lymphatic Filariasis disease in Jati Sampurna, West Java Indonesia. The model assumes that acute infected humans are infectious and treatment is given to a certain number of acute infected humans found from screening process. The treated acute individuals are assumed to be remain susceptible to the disease. The model is analyzed and it is found a condition for the existence and stability of the endemic equilibrium. A well known rule of thumb in epidemiological model, that is, the endemic equilibrium exists and stable if the basic reproduction number is greater than one, is shown. Moreover, it is also shown that if the level of screening n is sufficiently large, current medical treatment strategy will be able to reduce the long-term level of incidences. However, in practice it is not realistic and cannot eliminate the disease, in terms of reducing the basic reproduction number. The reproduction number can be reduced by giving additional treatments, such as reducing the biting rate and mosquito's density. This suggests that there should be a combination of treatment to eliminate the disease.
ABSTRACT It has been indicated that a long term application of combined mass drug treatment may c... more ABSTRACT It has been indicated that a long term application of combined mass drug treatment may contribute to the development of drug resistance in lymphatic filariasis. This phenomenon is not well understood due to the complexity of filaria life cycle. In this paper we formulate a mathematical model for the spread of mass drug resistant in a filaria endemic region. The model is represented in a 13-dimensional Host-Vector system. The basic reproductive ratio of the system which is obtained from the next generation matrix, and analysis of stability of both the disease free equilibrium and the coexistence equilibria are shown. Numerical simulation for long term dynamics for possible field conditions is also shown.
In 2000 WHO had issued a Global Program to Eliminate Lymphatic Filariasis by 2020. Lymphatic Fila... more In 2000 WHO had issued a Global Program to Eliminate Lymphatic Filariasis by 2020. Lymphatic Filariasis is an infectious disease that may cause permanent disability to the infected human. This disease is caused by parasitic worms and transmitted by mosquitoes. In the acute cases, the infected persons will undergo swelling in parts of their body. One of the treatment which has been successfully implemented in some countries is the Diethylcarbamazine (DEC) mass treatment. This treatment, which was implemented every ...
ABSTRACT The Blue Mountains Water Skink, Eulamprus leuraensis, is listed as an endangered species... more ABSTRACT The Blue Mountains Water Skink, Eulamprus leuraensis, is listed as an endangered species under the IUCN Red List. This lizard species has a typical characteristic of growth with a low fecundity. It is known that the offspring quality may decline with maternal age of the parents despite they can grow rapidly from neonatal size to adult size within two to three years. It is also believed that low adult survival rates and specialization on rare and fragmented type of habitat are the main cause leading to the endangered status of the lizard. A mathematical model with age structure for Eulamprus leuraensis, taking into account the variation of survival rate in each structure and the declining of offspring quality with respect to maternal age is considered here. Stable coexistence of non-trivial equilibriumis shown. It is also shown that an endangered status is due to combination oflow reproductive output and low rates of adult survival. Further, understanding the age structure within populations can facilitate efective management of the endangered species.
ABSTRACT Aedes aegypti is the main vector of dengue disease in many tropical and sub-tropical cou... more ABSTRACT 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 the field.
In this paper, we discuss a two-age-classes dengue transmission model with vaccination. The reaso... more In this paper, we discuss a two-age-classes dengue transmission model with vaccination. The reason to divide the human population into two age classes is for practical purpose, as vaccination is usually concentrated in one age class. We assume that a constant rate of individuals in the child-class is vaccinated. We analyze a threshold number which is equivalent to the basic reproduction number. If there is an undeliberate vaccination to infectious children, which worsens their condition as the time span of being infectious increases, then paradoxically, vaccination can be counter productive. The paradox, stating that vaccination makes the basic reproduction number even bigger, can occur if the worsening effect is greater than a certain threshold, a function of the human demographic and epidemiological parameters, which is independent of the level of vaccination. However, if the worsening effect is to increase virulence so that one will develop symptoms, then the vaccination is always productive. In both situations, screening should take place before vaccination. In general, the presence of class division has obscured the known rule of thumb for vaccination.
ABSTRACT This paper presents a model of tuberculosis transmission with vaccination by explicitely... more ABSTRACT This paper presents a model of tuberculosis transmission with vaccination by explicitely considering the total number of recovered individuals, either from natural recovery or due to vaccination. In this paper the endemic and nonendemic fixed points, basic reproduction number, and vaccination reproduction number are given. Some results regarding the stability of the fixed points and the relation to the basic reproduction numbers are analysed. At the end of this study, the numerical computation presented and it shows that vaccination is capable to reduce the number of laten and infectious populations.
ABSTRACT In this paper we formulate a model of dengue fever transmission by considering the prese... more ABSTRACT In this paper we formulate a model of dengue fever transmission by considering the presence of asymptomatic and symptomatic compartments. The model takes the form as a system of differential equations representing a host-vector SIR (Susceptible - Infective -Recovered) disease transmission. It is assumed that both host and vector populations are constant. It is also assumed that reinfection of recovered hosts by the disease is possible due to a wanning immunity in human body. We analyze the model to determine the qualitative behavior of the model solution and use the concept of effective basic reproduction number (fraktur Rp) as a control criteria of the disease transmission. The effect of mosquito biting protection (e.g. by using insect repellent) is also considered. We compute the long-term ratio of the asymptomatic and symptomatic classes and show a condition for which the iceberg phenomenon could appear.
In this paper we present a deterministic, discrete-time model for a two-patch predator-prey metap... more In this paper we present a deterministic, discrete-time model for a two-patch predator-prey metapopulation. We study optimal harvesting for the metapopulation using dynamic programming. Some rules are established as generalizations of rules for a single-species metapopulation harvesting theory. We also establish rules to harvest relatively more (or less) vulnerable prey subpopulations and more (or less) efficient predator subpopulations.
Uploads
Papers by aldi supriatna