C H A P T E R 7

Mathematical Models and

Optimal Control in Mosquito

Transmitted Diseases

Peyman Ghaffari

Chair of IMAAC (COST Action CA 16227) &

Center for Research and Development in Mathematics and Applications (CIDMA),

Department of Mathematics, University of Aveiro, Aveiro, Portugal

Cristiana J. Silva

Center for Research and Development in Mathematics and Applications (CIDMA),

Department of Mathematics, University of Aveiro, Aveiro, Portugal

Delfim F. M. Torres

Center for Research and Development in Mathematics and Applications (CIDMA),

Department of Mathematics, University of Aveiro, Aveiro, Portugal

CONTENTS

7.1

Introduction ...............................................................

143

7.2

Controlled model ..........................................................

145

7.3

Optimal control problem ..................................................

147

7.4

Numerical results and discussion ..........................................

148

7.A

Unique Optimal Solution ..................................................

155

7.1

INTRODUCTION

Understanding, predicting, and mitigating the spread of mosquito-borne diseases, in

diverse populations and geographies, poses several modeling challenges. In fact, despite

centuries of enormous efforts, mosquito-borne diseases continue to cause significant pub-

lic health burden and are widely re-emerging or emerging [27, 30]. Here our focus is on

mathematical models in mosquito transmitted diseases. Such models can be classified in

different classes, e.g., agent-based models [27]; networks [49]; models described by sys-

tems of ordinary differential equations [14, 35]; by fractional order differential equations

[16, 43]; reaction–diffusion equations [4, 56]; or discrete systems [9, 24]. They also apply

DOI: 10.1201/9781003035992-7

143