A contribution to the mathematical theory of epidemics

Abstract

(1) One of the most striking features in the study of epidemics is the difficulty of finding a causal factor which appears to be adequate to account for the magnitude of the frequent epidemics of disease which visit almost every population. It was with a view to obtaining more insight regarding the effects of the various factors which govern the spread of contagious epidemics that the present investigation was undertaken. Reference may here be made to the work of Ross and Hudson (1915-17) in which the same problem is attacked. The problem is here carried to a further stage, and it is considered from a point of view which is in one sense more general. The problem may be summarised as follows: One (or more) infected person is introduced into a community of individuals, more or less susceptible to the disease in question. The disease spreads from the affected to the unaffected by contact infection. Each infected person runs through the course of his sickness, and finally is removed from the number of those who are sick, by recovery or by death. The chances of recovery or death vary from day to day during the course of his illness. The chances that the affected may convey infection to the unaffected are likewise dependent upon the stage of the sickness. As the epidemic spreads, the number of unaffected members of the community becomes reduced. Since the course of an epidemic is short compared with the life of an individual, the population may be considered as remaining constant, except in as far as it is modified by deaths due to the epidemic disease itself. In the course of time the epidemic may come to an end. One of the most important probems in epidemiology is to ascertain whether this termination occurs only when no susceptible individuals are left, or whether the interplay of the various factors of infectivity, recovery and mortality, may result in termination, whilst many susceptible individuals are still present in the unaffected population. It is difficult to treat this problem in its most general aspect. In the present communication discussion will be limited to the case in which all members of the community are initially equally susceptible to the disease, and it will be further assumed that complete immunity is conferred by a single infection.

Towards malaria control and elimination in Ghana: challenges and decision making tools to guide planning

“…Modifying the Kermack–Makendrick model,[30] a susceptible, infected, recovered/removed susceptible (SIRS) model was used to describe the transmission dynamics of malaria in a municipality in the forest region of Ghana. [31] Municipal-level health facility reported malaria cases were used to fit the model in 2014, which involved investigating the prevalence of malaria and also determining the disease-free equilibrium state for the Techiman municipality.…”

Estimating infection prevalence: Best practices and their theoretical underpinnings

“…This measure describes the occurrence of a pathogen in a population and is an essential component of mathematical models in epidemiology (Kermack & McKendrick, 1927). Because determining the “true” prevalence of a pathogen in a population would require exhaustive sampling from every individual in the target population, studies generally estimate pathogen prevalence by determining the infection status of a proportion of the population via necropsy or sampling of feces, urine, blood, or saliva (Jovani & Tella, 2006).…”

A mobility model for classical swine fever in feral pig populations

“…The model consists of: a gridded landscape of 1 km 2 cells with some containing permanent water sources (see Figure 1); herds having a type (adult male or family), home-range, current location and current disease state, susceptible (S), exposed (E), infectious (I ), recovered (R 1 ) or removed (R 2 ) [22]; disease transmission and disease progress rules; and herd movement rules. and cross-hatching is used where both susceptible and infectious states are present.…”

“…Spatial simulation models have been developed in order to understand the time-course and changing spatial scale of an outbreak and the effect which targeted culling or vaccination may have [4,11,[20][21][22]. These models are generally focused on domestic animals, with some models capturing explicit animal movement between farms, saleyards and other locations where disease transmission may readily occur.…”