Аннотация
This paper develops and numerically investigates a dynamic model for assessing the effectiveness of digital marketing channels in promoting agricultural products in Kazakhstan. The model describes the joint evolution of brand awareness, customer base, and cumulative revenue under the influence of marketing investments and seasonal demand fluctuations. The core of the approach is a system of three nonlinear ordinary differential equations, where the state variables represent brand awareness A(t), number of active customers C(t), and cumulative revenue S(t). Digital channels are modeled through control functions ui (t), which affect both awareness and direct sales, while seasonality is represented by a sinusoidal component in the awareness equation. A numerical experiment is carried out for a 24 month planning horizon with a total digital marketing budget of 10 million KZT, equally and constantly allocated among three channels (search advertising, social media, and marketplaces). Under this baseline strategy, brand awareness increases from 100 to approximately 420 conditional units, the customer base grows from 50 to about 1 650 active customers, and cumulative revenue reaches around 1.4 billion KZT equivalent by the end of the period. The instantaneous revenue rate rises from about 1.3 million KZT per month at the beginning to over 40 million KZT per month by month 24. The obtained results demonstrate a pronounced time lag between awareness growth and revenue acceleration, a saturation effect in the customer base due to limited market capacity, and a strong seasonal modulation of short term performance. The proposed model provides a quantitative basis for scenario analysis and future optimal allocation of digital marketing budgets in the agri food sector of Kazakhstan. Keywords: digital marketing, agribusiness, agricultural products, Kazakhstan, dynamic modeling, system of differential equations, marketing budget optimization.