An Optimal Control Model to Understand the Potential Impact of the New Vaccine and Transmission-Blocking Drugs for Malaria: A Case Study in Papua and West Papua, Indonesia

Abstract

Malaria is one of the major causes of a high death rate due to infectious diseases every year. Despite attempts to eradicate the disease, results have not been very successful. New vaccines and other treatments are being constantly developed to seek optimal ways to prevent malaria outbreaks. In this article, we formulate and analyze an optimal control model of malaria incorporating the new pre-erythrocytic vaccine and transmission-blocking treatment. Sufficient conditions to guarantee local stability of the malaria-free equilibrium were derived based on the controlled reproduction number condition. Using the non-linear least square fitting method, we fitted the incidence data from the province of Papua and West Papua in Indonesia to estimate the model parameter values. The optimal control characterization and optimality conditions were derived by applying the Pontryagin Maximum Principle, and numerical simulations were also presented. Simulation results show that both the pre-erythrocytic vaccine and transmission-blocking treatment significantly reduce the spread of malaria. Accordingly, a high doses of pre-erythrocytic vaccine is needed if the number of infected individuals is relatively small, while transmission blocking is required if the number of infected individuals is relatively large. These results suggest that a large-scale implementation of both strategies is vital as the world continues with the effort to eradicate malaria, especially in endemic regions across the globe.

Assessing the Impact of Relapse, Reinfection and Recrudescence on Malaria Eradication Policy: A Bifurcation and Optimal Control Analysis

“…There are many mathematical models discussing malaria transmission, such as [ 4 , 14 , 15 , 17 , 21 , 23 ] and many more, but none of the mentioned references discuss the impact of relapse, recrudescence, and reinfection all together in one model. Recently, the authors of [ 29 ] introduced a complex nine-dimensional system of ordinary differential equations model to describe malaria transmission under the impact of relapse, recrudescence, and reinfection.…”

“…Aldila et al [ 4 ] considered vector-bias phenomena in their model and used an optimal control approach to find the best possible strategies to eradicate malaria. Several other mathematical models for malaria have also introduced the consideration of several factors, such as human mobility [ 16 ], control strategies [ 17 ], temperature [ 18 ], vector-bias [ 19 ], superinfection [ 20 ], seasonal factors [ 21 , 22 ], impact of vaccines and transmission-blocking drugs [ 23 ], social hierarchy [ 24 ], etc.…”

Enhancing Malaria Control Strategy: Optimal Control and Cost‐Effectiveness Analysis on the Impact of Vector Bias on the Efficacy of Mosquito Repellent and Hospitalization

“…We solve the model in (20) with and without control numerically by applying the backward and forward sweep as described in [45]. Readers who are interested to see further examples on the implementation of this algorithm may refer to [33,[46][47][48]. In the beginning, we give an initial guess for u 1 t and u 2 t constant for all time t. With this initial guess, we solve system (20) forward in time.…”

A Mathematical Approach for Analysing the Effects of Corruption on Transmission Dynamics of Malaria

“…Upaya pemahaman terhadap dinamika penyebaran penyakit telah banyak dilakukan termasuk dengan pendekatan matematika [2,3]. Penelitian-penelitian tersebut menganalisis dinamika penyebaran penyakit malaria untuk menganalisis pengaruh intervensi/strategi pencegahan seperti vaksinasi, fumigasi dan pengobatan [1,[4][5][6][7][8][9]. Sejauh ini, belum ada model matematika yang diformulasi untuk menganalisis pengaruh korupsi terhadap dinamika penyebaran penyakit malaria.…”