MODELLING THE EFFECTS OF SOCIAL FACTORS ON POPULATION DYNAMICS USING AGE-STRUCTURED MODEL AS A MANAGEMENT STRATEGY

Abstract

This study used an age-structured model was used to investigate the effects of social factors to population dynamics. Apart from age, subset of time affecting the population dynamics of human beings, other social factors also contribute to this human population dynamic. Examples of such social factors includes food supply, level of education, availability of suitable shelter, level of poverty and availability of universal health care. The modified age-structured mathematical model was developed, with partial differential equations that consisted of three variables of age, time and social factors. The model was developed to predict the future population size using disjoint age groups namely: infants, juvenile, sub-adults, adults and old persons. In this study, the population dynamics was modelled, where population was put into age–structures and the transition rate was incorporated into new modified model. Method of separation of variables was applied to find the analytic solutions of the new modified age-structured model developed while method of Finite Difference Method (FDM) was used to discretize formulated mathematical model in both absence and presence of social factors. The two discretised forms of models were analytically solved using closed form iteration method. The Kenya Population Data 2019, was numerically substituted into the modified mathematical model using MATLAB, and the system numerically computed. The stability and the convergence of the discretised mathematical model obtained by Finite Difference Method was established using the Crank-Nicolson scheme and the condition for stability was obtained to be 𝛾 ≤ 1 2 and ∆𝛼 = 1. Numerical simulation in absence of social factors 𝛿 = 0, generated a triangular population pyramid, a characteristic of high birth rate, and high mortality rate and solutions obtained indicated that, the population is unstable, meanwhile the economic dependency ratio was obtained to be 1:2. Whereas with improved implementation of social factors 𝛿 > 0, the population stabilized at an optimum of 𝛿 ≥ 0.75, and the economic dependency ratio improved to 1:1.14, implying that, support by independent population towards the dependent population decreased. This results indicated that the social factors affects the mortality rate inversely and the birth rate and net-migration rates are affected directly, that is; the improvement in the provision of social factors leads to an increase in both birth and migration rates, and population structure gives a square population pyramid with characteristics of low birth rate and low mortality rate, like that of developed countries. Using social factors as population management strategy, the provision of social factors at an efficacy of = 0.75 , yields a lower birth rate of 𝛽𝑜𝑝𝑡 = 0.05104 down from 𝛽𝑜𝑙𝑑 = 0.05178 and a lower mortality rate of 𝜇𝑜𝑝𝑡 = 0.00184 from 𝜇𝑜𝑙𝑑 = 0.02786. The findings of obtained suggests a new method of managing and stabilizing population using social factors. The model also predicts the limiting optimal population size to be achieved due to improvement of social factors as 57,956,100 to be realized in 2054 after 35 years, up from 38,589,011 in 2019.