Modelling malaria dynamics with partial immunity and protected travellers: optimal control and cost-effectiveness analysis

Abstract

A mathematical model of malaria dynamics with naturally acquired transient immunity in the presence of protected travellers is presented. The qualitative analysis carried out on the autonomous model reveals the existence of backward bifurcation, where the locally asymptotically stable malaria-free and malaria-present equilibria coexist as the basic reproduction number crosses unity. The increased fraction of protected travellers is shown to reduce the basic reproduction number significantly. Particularly, optimal control theory is used to analyse the non-autonomous model, which incorporates four control variables. The existence result for the optimal control quadruple, which minimizes malaria infection and costs of implementation, is explicitly proved. Effects of combining at least any three of the control variables on the malaria dynamics are illustrated. Furthermore, the cost-effectiveness analysis is carried out to reveal the most cost-effective strategy that could be implemented to prevent and control the spread of malaria with limited resources.

Global stability and cost-effectiveness analysis of COVID-19 considering the impact of the environment: using data from Ghana

“…The cost benefits associated with the implementation of the control strategies can be compared through cost-effectiveness analysis. Thus, following the approach used in several previous studies [53] , [54] , [55] , [56] , the incremental cost-effectiveness ratio (ICER) is calculated to determine the most cost-effective strategy of all the different control intervention strategies considered in this work. Most often, ICER is employed to measure up the changes between the costs and the health benefits of any two different control intervention strategies i and j competing for the same limited resources.…”

Mathematical modelling and optimal cost-effective control of COVID-19 transmission dynamics

“…where, λ i , i = 1, 2, 3, ..., 7, represent the adjoint variables associated with the state variables of the model (5). The standard existence result for minimizing control problem as appeared in [43,44] is adapted as follows.…”

How to coordinate vaccination and social distancing to mitigate SARS-CoV-2 outbreaks

“…Optimal control of such models is an active research topic, and both generalized interaction models [4] time-optimal policies [8, 25], and stochastic compartmental models [48] have been considered. Additionally, optimal mitigation policies have been proposed for several diseases, including dengue fever [18] and malaria [39]. Throughout 2020, many researchers have proposed compartmental models for predicting the impact of countermeasures on the spread of SARS-CoV-2 [20, 49].…”