Some mathematical tools for modelling malaria: a subjective survey

Abstract

In this paper, we provide a brief survey of mathematical modelling of malaria and how it is used to understand the transmission and progression of the disease and design strategies for its control to support public health interventions and decision-making. We discuss some of the past and present contributions of mathematical modelling of malaria, including the recent development of modelling the transmission-blocking drugs. We also comment on the complexity of the malaria dynamics and, in particular, on its multiscale character with its challenges and opportunities. We illustrate the discussion by presenting a curve fitting using a 95% confidence interval for the South African data for malaria from the years 2001-2018$ and provide projections for the number of malaria cases and deaths up to the year 2025.

On a Stochastic Approach to Extensions of the Susceptible‐Infected‐Susceptible (SIS) Model Applied to Malaria

“…Since malaria provides temporary immunity and is not lethal if treated, it is possible to use a SIRS (Susceptible-Infected-Recovered-Susceptible) model, since recovered individuals return to the S class with probability p p > 0 or relapsed individuals become infected again with probability 1 − p. So to Ross's S h I h S h -S v I v S v model, we add the R recovered compartment. These types of model are also solved in [17,18]. Figure 2 illustrates the scheme of disease progression.…”

“…The disease-free equilibrium (DFE) of this model is therefore N, 0, 0 . Authors such as [17,19,20] have also studied these types of models.…”