Modelling of Malaria Transmission Using Delay Differential Equation

Abstract

Malaria is one of the major causes of deaths and ill health in endemic regions of sub-Saharan Africa and beyond despite efforts made to prevent and control its spread. Epidemiological models on how malaria is spread have made a substantial contribution on the understanding of disease changing aspects. Previous researchers have used Susceptible -Exposed-Infectious-Recovered (SEIR) model to explain how malaria is spread using ordinary differential equations. In this paper we develop mathematical SEIR model to define the dynamics of the spread of malaria using Delay differential equations with four control measures such as long lasting treated insecticides bed nets, intermittent preventive treatment of malaria in pregnant women (IPTP), intermittent preventive treatment of malaria in infancy (IPTI) and indoor residual spraying. The model is analyzed and reproduction number derived using next generation matrix method and its stability is checked by Jacobean matrix. Positivity of solutions and boundedness of the model is proved. We show that the disease free equilibrium is locally asymptotically stable if R 0 <1 (R 0 -reproduction number) and is unstable if R 0 >1. Numerical simulation shows that, with proper treatment and control measures put in place the disease is controlled.

Delays in Plant Virus Models and Their Stability

“…Processes with delay times can be modeled using delay differential equations (DDEs). DDEs have been used to model time delays in virus propagation models, for example in [13,14]. For viruses in plants, DDEs have also been used, for example in [15][16][17].…”

Effect of Environmental Immunity on Mathematical Modeling of Malaria Transmission between Vector and Host Population

“…Children under 5 accounted for about 80 percent of these deaths WHO (2023). A parasite known as Plasmodium is responsible for causing Malaria, which can infect human beings and female anopheles' mosquitoes alike Kipkirui et al, (2020). There are four primary varieties of Plasmodium: Plasmodium falciparum, Plasmodium malaria, Plasmodium oval, and Plasmodium vivax.…”