A mathematical model of malaria and the effectiveness of drugs

Abstract

We propose a new deterministic model for the dynamics of malaria and the effectiveness of drugs and the positivity of the model investigated. The human population was portioned into three distinct compartments of susceptible, infected and the recovered, while the mosquito population was portioned into two distinct Compartments of susceptible and the infected, giving rise to a set of five ordinary differential equations. A parameter (A) is introduced to measure the effectiveness of anti malarial drugs in the infected compartment. The dynamics of the model was obtained. It was observed that both the disease free equilibrium states will be stable if () A > 60% and if the mosquitoes population is reduced the human population will also be stable. Numerical simulations were presented to show some results

A new fractional SIRS-SI malaria disease model with application of vaccines, antimalarial drugs, and spraying

“…1 Department of Mathematics, University of Rajasthan, Jaipur, India. 2 Department of Mathematics, JECRC University, Jaipur, India. 3 Department of Mathematics, College of Science, King Saud University, Riyadh, Saudi Arabia.…”

“…Agusto et al [1] reported a SIR having infection rate of nonlinear type with the aid of vaccination for the human population. Abdullahi et al [2] analyzed the outcomes of treatment as a control variable on the malaria transmission process. Mandal et al [3] formulated the mathematical representation of malaria transmission with the situation of person-to-person transmission via blood transfusions and malaria-infected ladies having pregnancy.…”

Model Matematika Sis-Si Dalam Penyebaran Penyakit Malaria Dengan Vaksinasi Taksempurna

“…Penelitian ini bertujuan untuk memodifikasi model SIR-SI dari Abdullahi [1] menjadi model SIS-SI dengan melihat efek dari vaksinasi taksempurna. Model epidemi dengan vaksinasi taksempurna mengacu pada model Safan [10].…”

Sirs-Si Model of Malaria Disease with Application of Vaccines, Anti-Malarial Drugs, and Spraying

“…The effect of treatment as a control variable on malaria transmission system was studied in the framework of optimal control theory by [2]. Model of malaria transmission was investigated in [3] by considering the existence of human-to-human transmission through blood transfusions and through malariainfected pregnant women (congenital).…”

“…In this current work, we discuss the effectiveness of the use of drugs in a malaria transmission model based on [3]. Modification of the model is done by considering the assumption that humans belong to recovered class have possibility to be susceptible, i.e., we consider a SIRS-SI model [4].…”