Boom! Mathematical Models for Population Growth

2003 ◽  
pp. 117-142
Author(s):  
Mohammad Moazzam ◽  
Richard H. Schwartz
Keyword(s):  
Population Growth ◽  
Mathematical Models

Theoretical basis for the use of pathogens as biological control agents of pest species

Parasitology ◽  
1982 ◽  
Vol 84 (4) ◽  
pp. 3-33 ◽  
Author(s):  
R. M. Anderson
Keyword(s):  
Population Growth ◽  
Mathematical Models ◽  
Horizontal Transmission ◽  
Host Density ◽  
Host Population ◽  
Pest Species ◽  
Population Abundance ◽  
Pest Population ◽  
Insect Pathogen ◽  
Cyclic Changes

SUMMARYThe population dynamics of insect–pathogen interactions are examined with the aid of simple mathematical models. Three concepts of central importance to the interpretation of population behaviour are discussed, namely the ability of the pathogen to persist within its host population, the ability to regulate and depress host population abundance, and the ability to induce non-seasonal cyclic changes in host density. The selection of pathogen species or strains to depress pest population growth is discussed and the optimal characteristics are shown to be intermediate pathogencity combined with an ability to reduce infected host reproduction, high transmission efficiency, including elements of vertical as well as horizontal transmission stages. When the pathogen plays a significant role in the regulation of host population growth, it is argued that many insect–pathogen interactions will exhibit non-seasonal oscilations in host and pathogen abundance. Mathematical models are used to explore the patterns of population behaviour that result from the continual introduction of a pathogen into a target pest population. It is shown that there exists a critical introdution rate, above which the eradication of the pest is theoretically possible. Significant reductions in pest population abundance will not occur until the introduction rate approaches this critical value, whereupon the oscillatory behaviour of the interaction between host and pathogen population will be suppressed.A general dicussion is given of the problems arising from the combined use of chemical agents and pathogens for the control of pest species, and the evolutionary pressures acting on host and pathogen populations.

scholarly journals Modeling of the relationship between the Earth population growth and the electric energy production processes

2021 ◽  
Vol 16 (4) ◽  
pp. 110-121
Author(s):  
Valeriy P. Kavchenkov ◽  
◽  
Elena V. Kavchenkova ◽  
Ivan D. Chernenkov ◽  
◽  
...  
Keyword(s):  
Population Growth ◽  
Mathematical Models ◽  
Growth Rates ◽  
Inflection Point ◽  
Electric Energy ◽  
Electricity Production ◽  
World Population ◽  
The Earth ◽  
The World ◽  
Per Capita

The actual problem of an adequate mathematical description of the world development global processes trends is studied on the example of the Earth population growth and the production (consumption) of the electric energy. Various models used to describe the past, present and future of the various processes in nature, technology and economics are considered. It is shown that these processes are well described by the equations obtained during solving differential models with exponentially growth rates decaying in time. These models take into account the currently accepted doctrine of sustainable development of the world system using energy saving technologies, preserving environmental safety and using renewable energy sources. The similarity of the studied global processes and the possibility of their description by one criterion equation are established. At the same time their dynamics is characterized by different speeds. The first period is characterized by a rapid growth. After the inflection point the growth rates slow down but the volumes increase significantly and a gradual saturation occurs. The influence of the model parameters on the character of the studied processes on the phase plane is estimated which significantly simplifies their analysis. It is shown that the process of the world population growth passed the inflection point in 1990 and is 29 years ahead of the world electricity production growth. But the growth rates of electricity production and its consumption per capita are significantly higher. Thus, new mathematical models are proposed to describe the dynamic series of the Earth population growth, world production and electric energy consumption per capita. The obtained mathematical models have been in good agreement with statistical data for 60 years since 1960 and have high values of the determination coefficient. The studied processes prediction for the long-term period up to 2050 was made with their help. The results of the prediction do not contradict the results of other authoritative studies using the global processes inertial development model.

Experimental studies of age-prevalence curves forSchistosoma mansoniinfections in populations ofBiomphalaria glabrata

Parasitology ◽  
1984 ◽  
Vol 89 (1) ◽  
pp. 79-106 ◽  
Author(s):  
R. M. Anderson ◽  
Jenny Crombie
Keyword(s):  
Population Growth ◽  
Mathematical Models ◽  
Intermediate Host ◽  
Age Structure ◽  
Death Rate ◽  
Experimental Studies ◽  
Biomphalaria Glabrata ◽  
Force Of Infection ◽  
Laboratory Populations ◽  
Per Capita

SummaryWe report the results of experimental studies of the generation of age-prevalence curves forSchistosoma mansoniinfections in laboratory populations ofBiomphalaria glabrata. Within snail populations of varying sizes and age structures, the net force of infection is shown to be linearly dependent on the rate at which miracidia are introduced into the aquatic habitat of the host. For individual snails, the per capita force of infection is shown to be related to snail age and size, and the death rate of shedding snails is demonstrated to be dependent on the period of time during which a snail has been releasing cercariae. Both factors are important determinants of the proportion of infected snails within populations of hosts and may generate convex age-prevalence curves. Comparisons of snail abundance in populations either exposed, or not exposed, to infection suggest thatS. mansonican act to significantly depress the population growth of its intermediate host. Mathematical models are developed, encorporating the age structure of snail populations, to aid in the interpretation of experimental results.

On habit and habitat

2021 ◽  
Vol 477 (2247) ◽  
Author(s):  
Peter Vadasz ◽  
Alisa S. Vadasz
Keyword(s):  
Population Growth ◽  
Mathematical Models ◽  
Resource Utilization ◽  
Predictive Modelling ◽  
Scientific Theories ◽  
Initial Development ◽  
Experimental Knowledge ◽  
Natural Behaviour ◽  
Biological Interpretation

Scientific theories based on mathematical models are frequently used in sciences to reveal natural behaviour of systems and eventually to be able in predicting such behaviour once the system's parameters and relevant conditions are known and can be specified. The integration of accumulated theoretical as well as experimental knowledge allows us to present such a unifying theory underlying the equivalence between habit and habitat in population growth. While the focus of the initial development was derived from microorganisms, the theory is extended to other population types too. The biological interpretation of ‘inertia’ or ‘habit’-based processes is provided as a consequence of this theory, and its relationship to the population ‘resource utilization’ available in the ‘habitat’ is derived. This paper focuses on the link between the ‘resource utilization’, which is related to the ‘habitat’, and ‘biological inertia’, which is related to population ‘habit’. This link extends the context of population growth and predictive modelling of microorganisms.

EFFECTS OF SOME CONSTANT AND ALTERNATING TEMPERATURES ON POPULATION GROWTH OF THE PEA APHID, ACYRTHOSIPHON PISUM (HOMOPTERA: APHIDIDAE)

1973 ◽  
Vol 105 (1) ◽  
pp. 145-156 ◽  
Author(s):  
W. H. Siddiqui ◽  
C. A. Barlow ◽  
P. A. Randolph
Keyword(s):  
Population Growth ◽  
Mathematical Models ◽  
Acyrthosiphon Pisum ◽  
Pea Aphid ◽  
Average Deviation ◽  
Image Position ◽  
Faster Development ◽  
Growth And Reproduction

AbstractAlternating temperatures resulted in higher intrinsic rates of increase (rm) than constant temperatures within the range of temperature favourable for growth and reproduction of the pea aphid. This difference was due to slightly faster development and earlier attainment of maximum fecundity at alternating temperatures.Preliminary mathematical models relating rm to constant and alternating temperatures are derived. These are:for constant temperatures andfor alternating temperatures of 5°, 10°, and 15° amplitudes respectively. Average deviation between empirical and computed values is 2%. The efficacy of these models is restricted to temperatures favourable for development and reproduction of the pea aphid.

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