Rachelle Miron

Bio: Rachelle Miron is an academic researcher. The author has an hindex of 1, co-authored 1 publications receiving 5 citations.

Impulsive Differential Equations with Applications to Infectious Diseases

Abstract: Impulsive differential equations are useful for modelling certain biological events. We present three biological applications showing the use of impulsive differential equations in real-world problems. We also look at the effects of stability on a reduced two-dimensional impulsive HIV system. The first application is a system describing HIV induction-maintenance therapy, which shows how the solution to an impulsive system is used in order to find biological results (adherence, etc). A second application is an HIV system describing the interaction between T-cells, virus and drugs. Stability of the system is determined for a fixed drug level in three specific regions: low, intermediate and high drug levels. Numerical simulations show the effects of varying drug levels on the stability of a system by including an impulse. We reduce these two models to a two-dimensional impulsive model. We show analytically the existence and uniqueness of T-periodic solutions, and show how stability changes when varying the immune response rate, the impulses and a certain nonlinear infection term. The third application shows how seasonal changes can be incorporated into an impulsive differential system of Rift Valley Fever, and looks at how stability may differ when impulses are included. The analysis of impulsive differential systems is crucial in developing more realistic mathematical models for infectious diseases.

Ulam’s-Type Stability of First-Order Impulsive Differential Equations with Variable Delay in Quasi–Banach Spaces

Abstract: Abstract In this paper, Ulam’s-type stabilities are studied for a class of first-order impulsive differential equations with bounded variable delays on compact interval with finite number of impulses. Results of stability are proved via newly established integral inequality of Bellman–Grönwall–Bihari type with delay for discontinuous functions. Using this inequality for the first time and assumption of α$\alpha$-Ho¨$\ddot{o}$lder’s condition instead of common Lipschitz condition is novelty of this paper. Moreover, solution is obtained in quasi–Banach spaces which is best suited for obtaining results under the assumptions of α$\alpha$-Ho¨$\ddot{o}$lder’s condition.

On Periodic Solutions of Delay Differential Equations with Impulses

Abstract: The purpose of this paper is to study the nonlinear distributed delay differential equations with impulses effects in the vectorial regulated Banach spaces R ( [ − r , 0 ] , R n ) . The existence of the periodic solution of impulsive delay differential equations is obtained by using the Schaffer fixed point theorem in regulated space R ( [ − r , 0 ] , R n ) .

An open approach to AIDS. Uganda.

Abstract: Uganda has one of the worst AIDS epidemics in the world and the number of cases is doubling every 4-6 months; yet it has done much to halt the spread of the disease. Uganda has had a vigorous AIDS education campaign since 1986. It is the only country in the world to carry out a national serosurvey to determine the prevalence of the virus. HIV-positive individuals run a counseling service. The Protestant and Catholic churches have launched anti-AIDS drives stressing sexual fidelity for the healthy compassion and care for the sick. President Yoweri Museveni had instructed the Ministry of Health to mobilize the educational and awareness campaign to correct the misconceptions of the people regarding AIDS. The campaigns have used leaflets posters radio schools political cadres the army and local civic action groups to spread the word in Ugandas many vernaculars. All have stressed that that untested blood transfusions and dirty needles can pass the virus as can mothers to newborns. They have emphasized that AIDS cannot be caught from shaking hands sharing cups or bedding or from mosquitoes. The AIDS Support Organization a volunteer group of HIV/AIDS infected persons has been established to respond to the needs of those who are infected or looking for accurate information. Although the campaign was constrained by limited financial resources the government never saw this as an obstacle in their goal and it is now being used as a model in other African countries.

Uganda battles AIDS on all fronts. Medical aid.

Abstract: This article reports the efforts undertaken by Uganda in preventing the spread of AIDS. AIDS cases were first reported in the country in 1982 which have spread along the main trade routes and all urban areas. During a world AIDS conference in June 1991 President Museveni urged African leaders to develop and implement AIDS programs to fight the disease. Uganda has been one of the first countries to develop a 5-year plan for the control and prevention of AIDS. This includes surveillance safe blood supply specific research patient care and public education. Comprehensive health information campaigns were also carried out. Another achievement is the establishment of a laboratory with tested blood products in 1988. Moreover the success of an anonymous HIV test program conducted in Kampala has encouraged authorities to extend the service throughout the country. Despite all these efforts however AIDS continues to spread in Uganda.