Abstract
In this paper, we develop and analyze an SIS-type epidemiological-mathematical model of the interaction between pesticide use and infectious respiratory disease transmission for investigating the impact of pesticide intoxication on the spread of these types of diseases. We further investigate the role of educational treatment for appropriate pesticide use on the transmission dynamics. Two impulsive control events are proposed: pesticide use and educational treatment. From the proposed model, it was obtained that the rate of forgetfulness towards educational treatment is a determining factor for the reduction of intoxicated people, as well as for the reduction of costs associated with educational interventions. To get reduced intoxications, the population’s fraction to which is necessary to apply the educational treatment depends on its individual effectiveness level and the educational treatments’ forgetfulness rate. In addition, the turnover of agricultural workers plays a fundamental role in the dynamics of agrotoxic use, particularly in the application of educational treatment. For illustration, a flu-like disease with a basic reproductive number below the epidemic threshold of 1.0 is shown can acquire epidemic potential in a population at risk of pesticide exposure. Hence, our findings suggest that educational treatment targeting pesticide exposure is an effective tool to reduce the transmission rate of an infectious respiratory disease in a population exposed to the toxic substance.
Highlights
Pesticides are chemical substances widely used in agriculture to control, prevent or eradicate pests of insects, birds, rodents, bacteria, herbs, among others [1]
Concerning the selected values of β and γ, which correspond to the rates associated with the disease, and d to the rate of exit from the system, they were selected so that the basic reproductive number of the disease without the presence of pesticides, that is, the classic basic reproductive number of an SIS (Rc0 1⁄4 b=ðg þ dÞ) model is less than one [38, 45]
Because we want to explore the impact that pesticide poisoning has on the development of this type of disease, we have assigned the value of βP greater than that of β
Summary
Pesticides are chemical substances widely used in agriculture to control, prevent or eradicate pests of insects, birds, rodents, bacteria, herbs, among others [1]. Educational treatment and infectious respiratory diseases: A mathematical model fetal malformations and cancer [3,4,5]. Following pesticide poisoning, the respiratory tract dilates [6, 7], so it is plausible to establish that being in the condition of poisoning makes one more susceptible to infectious respiratory diseases. We use mathematical modeling to investigate the transmission dynamics of respiratory infectious diseases after accounting for the link between pesticide exposure and increased susceptibility to acquiring the infection [8,9,10,11,12,13]
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