A mathematical model for the prediction of the prevalence of allergies in Zimbabwe

Caroline Mushayi; Farai Nyabadza; Esther Chigidi; Hope Mataramvura; Lorraine Pfavayi; Simbarashe Rusakaniko; Elopy Nimele Sibanda

doi:10.1016/j.waojou.2021.100555

A mathematical model for the prediction of the prevalence of allergies in Zimbabwe

World Allergy Organ J. 2021 Jun 25;14(7):100555. doi: 10.1016/j.waojou.2021.100555. eCollection 2021 Jul.

Authors

Caroline Mushayi^{1

2}, Farai Nyabadza³, Esther Chigidi¹, Hope Mataramvura^{2

4}, Lorraine Pfavayi^{2

5}, Simbarashe Rusakaniko⁶, Elopy Nimele Sibanda^{2

5}

Affiliations

¹ Midlands State University, Department of Mathematics, Senga Road, Gweru, Zimbabwe.
² Asthma, Allergy and Immune Dysfunction Clinic, 113 Kwame Nkrumah Ave., Harare, Zimbabwe.
³ University of Johannesburg, Department of Mathematics and Applied Mathematics, Auckland Park, Johannesburg, 2006, South Africa.
⁴ University of Zimbabwe; College of Health Sciences, Avondale, Harare, Zimbabwe.
⁵ National University of Science and Technology, NUST Medical School, Department of Pathology, Vera Road, Bulawayo, Zimbabwe.
⁶ University of Zimbabwe, College of Health Sciences, Department of Community Medicine, Avondale, Harare, Zimbabwe.

Abstract

Background: The prevalence of allergies has been observed to be increasing in the past years in Zimbabwe. It is thus important to consider the long term prevalence of allergies. Our interest is in investigating the trends of allergies in the next 2 decades.

Method: We formulate a deterministic model with 6 compartments to predict the prevalence of allergies in Zimbabwe. The human population is divided into 4 distinct epidemiological, classes based on their exposure to 2 allergen groups (food and inhalants), represented by 2 compartments. The model is used to predict the prevalence of allergen sensitization. The number of human allergen groups in each compartment are tracked through a system of differential equations. Model parameters were obtained by fitting observed data to the model. Graphical solutions of the model were developed using Matlab and Excel.

Results: The rate of sensitisation to food allergen sources is found to be lower than the rate of sensitisation to inhalant allergens. The rate at which individuals develop tolerance to food allergen sources is found to be almost twice the rate of developing tolerance to inhalant allergies. The equilibrium solutions (the long-term states of the populations) of the model are found to be non-zero implying that there will never be an allergy-free population. Our results also show that the prevalence of food allergy is likely to increase in the next 2 decades while inhalant allergy prevalence is expected to decrease.

Conclusion: Our long-term solutions show endemicity in allergies in Zimbabwe. So, allergy will be endemic in the Zimbabwean population; hence there is a need for allergy care and management facilities to be increased. These results are critical in policy development and planning around allergies in the near future.

Keywords: Food allergy; Inhalant allergy; Mathematical model; Zimbabwe.