1.1 The Prevention of Malaria
Ronald Ross is best known for being the first person to observe malaria parasites in a mosquito [18]. The event – on August 20\(^{th}\), 1897 in a military hospital in Hyderabad, India – is now celebrated as mosquito day. In the months that followed, Ross made the case that mosquitoes transmit malaria parasites [19]. Concurrently, the life-cycle of human malaria parasites was described by an Italian team, led by Giovanni Battista Grassi [20,21]. By 1899, a scientific consensus had formed among malaria experts that malaria was a mosquito-transmitted disease. It would take some time before the “mosquito hypothesis” was accepted more broadly.
The discoveries made by Ross and Battista Grassi closed a loop that Charles Laveran had opened in 1880 when he identified malaria parasites in blood, providing the first clear evidence that human malaria was a parasitic disease [22,23]. Laveran’s observation had spawned almost two decades of research describing malaria infections and disease in humans, all before the mode of transmission was known [24]. The modern view of the parasite life-cycle was not complete until the 1940s, through research describing the parasite’s liver stages by Garnham and colleagues [24,25].
Malaria is a disease that could be treated and measured before anyone knew what caused it or how it was transmitted. Malaria was commonly treated with quinine once the compound had been isolated in 1824. The chemical compound was isolated from the bark of Cinchona tree, which had been used to treat malaria fevers. The spleen rate, a reasonable metric for malaria was described by Dempster in 1948 [26]. All of this occurred before Laveran showed how that malaria was caused by infection with a parasite.
The elements of the story of malaria, including a full account of how the malaria parasite’s life cycle was unravelled over time is a topic that worth taking some time to learn [24,27–29].
Knowing the mode of transmission, the British military launched vector control efforts to protect British citizens from malaria in its colonial empire. At the time, vector control with bed nets and larval source management, and malaria was treated with quinine. Lest we imagine malaria control in this era was for general humanitarian purposes, Ross emphasizes population segregation as a useful mode of malaria control for the colonizers. Both Ross and Laveran were military doctors supporting colonial governments, a fact that we acknowledge that we can neither ignore nor excuse. We try to learn enough history to avoid repeating the same mistakes. We are sure to make enough mistakes of our own as we blunder forward.
In this first epoch of malaria control, it is Ross who once again draws our attention. After his big discovery, Ross turned his attention to malaria control. In 1910, he published a book, The Prevention of Malaria. A second second edition followed in 1911. Ross’s work on malaria prevention is of interest because he laid out a vision for a quantitative approach to the prevention of malaria. He clearly articulated how malaria control needed quantitative concepts, including well-developed metrics to measure malaria in populations. Ross himself developed the thick film, a technique that was intended to increase the sensitivity of malaria diagnostics [30,31]. In the service of understanding malaria for purposes of control, Ross developed the first mathematical models for malaria, in which he addressed basic questions about larval source management [16] and malaria transmission [1,17,32].
In the second decade of malaria control, the last phase of Ross’s career, he formed an alliance with Hilda Hudson, a mathematics professor from Cambridge University. Between 1915 and 1917, Ross and Hudson developed mathematical theory to support the study of epidemics, which they called a priori pathometry. Then, in 1921, Martini developed a model describing the dynamics of infections that immunized their hosts. In 1927, Kermack and McKendrick published the first of a five-part series on the mathematical theory of epidemics that described the dynamics of acute immunizing infections, which overshadowed the work by Ross and Hudson. Nowadays, the field is called mathematical epidemiology.
The parasite’s life-cycle has been an organizing principle for the study of malaria. The discoveries by Laveran, Ross, Battista Grassi, Garnham and others set the stage for hundreds of thousands of studies over 144 years (at the time of this writing) that have developed a rich and impressive body of knowledge. Over that time, we have learned an enormous amount about malaria and its control. The first comprehensive review of malaria, Malariology. A Comprehensive Survey of all Aspects of this Group of Diseases from a Global Standpoint, was published in 1949 in a two volume set edited by Mark F. Boyd with 70 chapters and 1643 pages from 65 contributors [33]. Almost 40 year later, 1988, the second comprehensive review of malaria was published in another two volume set, Malaria: Principles and Practice of Malariology, edited by Walter H Wernsdorfer and Sir Ian McGregor; this set had 57 chapters and 1818 pages from 68 contributors, [34]. Another 40 years has passed, and it is almost time for an update.
This book is a primer on mathematical models to support robust analytics for malaria policy (RAMP). It covers malaria epidemiology, mosquito ecology, human demography, and malaria transmission dynamics and control with a focus on the mathematical theory and models that have been developed over the past century. While this book will cover many of the topics in those two-volume sets, it is focused more narrowly on introducing the mathematical study of malaria that started with Ross. The field made some great leaps forward in the 1950s, when Macdonald wrote a series of papers that reviewed decades of field studies and updated Ross’s basic models. Macdonald’s paper on the sporozoite transformed the quantitative study of malaria transmission by mosquitoes, drawing attention to the importance of mosquito survival. In his next paper, Macdonald presented a formula for the basic reproductive number for malaria, an idea that almost certainly traces back to Alfred Lotka’s work in human demography. Macdonald would have known Lotka from his extensive work on Ross’s models of malaria. The simple mathematical models, now called the Ross-Macdonald model, thus defined basic theory for malaria transmission dynamics and control [2]. This book starts with the Ross-Macdonald model, and it covers a rich and wonderful set of models that has grown out of it. Around 1970, the mathematical study of malaria entered a period of elaboration through the work of Klaus Dietz, Norman TJ Bailey, Joan Aron, Barbara Hellriegel, and others. Ross was a pioneer in a field that has included important contributions by hundreds of scientists and analysts.
Nowadays, we can describe malaria as a managed, complex adaptive system involving non-linear interactions among mosquitoes, parasites, humans, and the managers. Malaria systems are heterogeneous and locally peculiar in some way: doing the same thing in different places can result in different outcomes. To understand why outcomes of malaria control vary, we need good theory for malaria, including malaria transmission intensity and seasonality, mosquito ecology and behaviors, mosquito and parasite genetics, health systems, and human behaviors. To give advice, we need malaria intelligence – information about these critical factors, and since the systems are peculiar, we will need local information to give tailored advice. We must grapple with questions about malaria that remain poorly understood, and we most offer advice even if there are enormous gaps in data and knowledge. We want to give policy advice that is robust to uncertainty. We will need well organized systems to store and analyze data and to develop intelligence that can help us learn and adapt. In all of these activities, mathematical models of malaria transmission dynamics and control play an important role. In this book, Applied Malaria Dynamics: Theory and Computation for Robust Analytics and Adaptive Malaria Control, we take a deep dive into dynamical systems models for malaria epidemiology, transmission dynamics, and control. It is designed to serve as an introduction and resource for malaria analysts who seek to use evidence and mathematical models to develop advice about malaria policies. We introduce the material using a modular framework for building malaria models designed to suppport RAMP [15]. Most of the examples use one of two RAMP-branded R packages: one is designed to build and solve systems of ordinary or delay differential equations ramp.xde; and the other supports discrete-time systems ramp.dts. These are further supported by other ramp software packages, including model libraries, and other simulation software that takes a deep dive into mosquito ecology, mosquito dispersal, malaria epidmiology (in the narrow sense). We also hope that the material can be used in scientific research.
To get all this started, we will walk through concepts as they developed over time, which brings us back to Ronald Ross, the study of the prevention of malaria, and the study of epidemics.1
References
The narrative in this book is often historical, which serves two purposes. First, it provides an excuse to cite and discuss old papers that should not get overlooked. Second, a historical narrative allows us to introduce malaria complexity in an ordered way, starting from principles that are simple and abstract, and progressing towards ideas that are non-linear, messy, or subtle. We will often use history as a way of structuring discussions, even as our attention turns increasingly to the mathematics we need to deal with the biological complexity of malaria in populations.↩︎