Basic Reproduction Number Research Papers (original) (raw)

Levels of parasitism and the dynamics of helminth systems is subject to the impact of environmental conditions such that we may expect long term increases in temperature will increase the force of infection and the parasite's basic... more

Levels of parasitism and the dynamics of helminth systems is subject to the impact of environmental conditions such that we may expect long term increases in temperature will increase the force of infection and the parasite's basic reproduction number, R0. We postulate that an increase in the force of infection will only lead to an increase in mean intensity of adults when adult parasite mortality is not determined by acquired immunity. Preliminary examination of long term trends of parasites of rabbits and grouse confirm these predictions. Parasite development rate increases with temperature and while laboratory studies indicate this is linear some recent studies indicate that this may be non-linear and would have an important impact on R0. Warming would also reduce the selective pressure for the development of arrestment and this would increase R0 so that in systems like the grouse and Trichostrongylus tenuis this would increase the instability and lead to larger disease outbr...

In epidemiological models of infectious diseases the basic reproduction number mathcalR_0{\mathcal{R}_0}mathcalR_0 is used as a threshold parameter to determine the threshold between disease extinction and outbreak. A graph-theoretic form of Gaussian... more

In epidemiological models of infectious diseases the basic reproduction number mathcalR_0{\mathcal{R}_0}mathcalR0 is used as a threshold parameter to determine the threshold between disease extinction and outbreak. A graph-theoretic form of Gaussian elimination using digraph reduction is derived and an algorithm given for calculating the basic reproduction number in continuous time epidemiological models. Examples illustrate how this method can be applied to compartmental models of infectious diseases modelled by a system of ordinary differential equations. We also show with these examples how lower bounds for mathcalR0{\mathcal{R}_0}mathcalR_0 can be obtained from the digraphs in the reduction process.

Abstract.We consider an SIR model with variable size population and formulate an optimal control problem subject to the model with vaccination and treatment as controls. Our aim is to find the optimal combination of vaccination and... more

Abstract.We consider an SIR model with variable size population and formulate an optimal control problem subject to the model with vaccination and treatment as controls. Our aim is to find the optimal combination of vaccination and treatment strategies that will minimize the cost of the two control measures as well as the number of infectives. Our model analyses show that the disease free equilibrium is globally asymptoti-cally stable if the basic reproduction number is less than unity while the endemic equilibrium exists and it is globally asymptotically stable whenever the basic reproduction number is greater than unity. We used Pon-tryagin’s maximum principle to characterize the optimal levels of the two controls. The resulting optimality system is solved numerically. The results show that the optimal combination of vaccination and treatment strategy required to achieve the set objective will depend on the relative cost of each of the control measures. The results from our simula...

These days, a lot of viruses spread in society causing the epidemic. One of them is the ZIKA virus. The transmission of ZIKA virus is mediated by a mosquito named Aedes aegypti or Aedes albopictus. The transmission of ZIKA virus can also... more

These days, a lot of viruses spread in society causing the epidemic. One of them is the ZIKA virus. The transmission of ZIKA virus is mediated by a mosquito named Aedes aegypti or Aedes albopictus. The transmission of ZIKA virus can also occur through the blood transfusion and sexual intercourse. In this study, the transmission of Zika virus to be discussed is only focused on the human population that the infected individuals can spread the ZIKA virus to susceptible individuals, and the transmission of ZIKA virus will be described in the SEIR mathematic model. From the obtained SEIR model results in two equilibrium points that are the virus free equilibrium point and the free viral equilibrium point. In addition, from the model analysis is obtained the basic reproduction number ℛ0. When ℛ0 < 1, the rate of ZIKA virus spread is smaller than the healing rate so that in the end the population of ZIKA virus infected individuals will be exhausted, and the ZIKA virus will be extinct. While at the time ℛ0 > 1, the infection rate of ZIKA virus is greater than the healing rate so that the spread of ZIKA virus will continue to occur and cause the endemic. Based on the stability analysis of the equilibrium point of the mathematic model of ZIKA virus spread, this is concluded that the virus free equilibrium point will be stable asymptotically local if ℛ0 < 1, and the free viral equilibrium point will be stable asymptotically local if ℛ0 >1.

We formulate and analyze Zika virus transmission model with three nonlinear forces of infection from infected mosquito, asymptomatic and symptomatic humans. The sensitivity indexes of the associated parameters of the model with respect to... more

We formulate and analyze Zika virus transmission model with three nonlinear forces of infection from infected mosquito, asymptomatic and symptomatic humans. The sensitivity indexes of the associated parameters of the model with respect to the basic reproduction number are calculated to identify intervention strategies for prevention and control of Zika virus. Multiple time-dependent optimal controls are considered. The analysis based on the use of optimal control theory made popular by Pontryagin's maximum principle is carried out, and the resulting optimality system is quantitatively simulated to investigate the impact of the controls on the dynamics of Zika virus. In addition, the effects of non-linearity of the forces of infection and other key parameters on the disease transmission are illustrated.

Geographical maps indicating the value of the basic reproduction number, R₀, can be used to identify areas of higher risk for an outbreak after an introduction. We develop a methodology to create R₀ maps for vector-borne diseases, using... more

Geographical maps indicating the value of the basic reproduction number, R₀, can be used to identify areas of higher risk for an outbreak after an introduction. We develop a methodology to create R₀ maps for vector-borne diseases, using bluetongue virus as a case study. This method provides a tool for gauging the extent of environmental effects on disease emergence. The method involves integrating vector-abundance data with statistical approaches to predict abundance from satellite imagery and with the biologically mechanistic modelling that underlies R₀. We illustrate the method with three applications for bluetongue virus in the Netherlands: 1) a simple R₀ map for the situation in September 2006, 2) species-specific R₀ maps based on satellite-data derived predictions, and 3) monthly R₀ maps throughout the year. These applications ought to be considered as a proof-of-principle and illustrations of the methods described, rather than as ready-to-use risk maps. Altogether, this is a first step towards an integrative method to predict risk of establishment of diseases based on mathematical modelling combined with a geographic information system that may comprise climatic variables, landscape features, land use, and other relevant factors determining the risk of establishment for bluetongue as well as of other emerging vector-borne diseases.

A vector-borne disease such as malaria has the potential to infect anyone regardless of the social classes to which the individuals belong, but the degree of disease transmission may be higher in one social class than the other. This... more

A vector-borne disease such as malaria has the potential to infect anyone regardless of the social classes to which the individuals belong, but the degree of disease transmission may be higher in one social class than the other. This paper presents and analyzes a time-dependent social hierarchy-structured deterministic model with a view to preventing and controlling the effects of social class disparity on the transmission dynamics of malaria disease in the interacting populations of humans and mosquitoes. The total human population is broadly stratified into low and high social classes with each consisting of three mutually exclusive compartments, namely susceptible, infectious and recovered humans with temporary immunity. The total vector population is subdivided into susceptible and infectious mosquitoes. The derived eight-dimensional system of differential equations is rigorously analyzed under optimal control framework with four control variables. Using Pontryagin's maximum principle, the existence of the control quadruple is proved. Efficiency analysis carried out shows that combination of all the controls is the most efficient intervention, while the costeffectiveness analysis reveals the most cost-effective single, double and triple interventions to curtail malaria spread in a social hierarchy-structured population.

Temperature is a key determinant of environmental suitability for transmission of human malaria, modulating endemicity in some regions and preventing transmission in others. The spatial modelling of malaria endemicity has become... more

Temperature is a key determinant of environmental suitability for transmission of human malaria, modulating endemicity in some regions and preventing transmission in others. The spatial modelling of malaria endemicity has become increasingly sophisticated and is now central to the global scale planning, implementation, and monitoring of disease control and regional efforts towards elimination, but existing efforts to model the constraints of temperature on the malaria landscape at these scales have been simplistic. Here, we define an analytical framework to model these constraints appropriately at fine spatial and temporal resolutions, providing a detailed dynamic description that can enhance large scale malaria cartography as a decision-support tool in public health. We defined a dynamic biological model that incorporated the principal mechanisms of temperature dependency in the malaria transmission cycle and used it with fine spatial and temporal resolution temperature data to eva...

Malaria can be eradicated from islands. To assess the prospects for eradication of malaria from the island of Príncipe in the Gulf of Guinea, we fitted a mathematical model to age-prevalence curves and thus obtained estimates of the... more

Malaria can be eradicated from islands. To assess the prospects for eradication of malaria from the island of Príncipe in the Gulf of Guinea, we fitted a mathematical model to age-prevalence curves and thus obtained estimates of the vectorial capacity and of the basic reproductive number (R0) for malaria. A cross-sectional malariological survey was carried out, in mid-1999, in six communities, comprising circa 17% of the total 6,000 population of the island. All houses in these communities were registered and their mode of construction recorded. Thick and thin blood films were prepared from all consenting individuals. Each individual was asked whether they possessed a mosquito net, whether they had slept under a mosquito net the previous night, whether they were allergic to chloroquine, and whether they had visited the main island of São Tomé since the beginning of the year. Outpatient records from March 1999 until the end of December 2000 were also examined and the age and place of...