In this paper, a deterministic compartmental eco-epidemiological model with optimal control of Newcastle disease (ND) in Tanzania is proposed and analysed. Necessary conditions of optimal control problem were rigorously analysed using Pontryagin's maximum principle and the numerical values of model parameters were estimated using maximum likelihood estimator. Three control strategies were incorporated such as chicken vaccination (preventive), human education campaign and treatment of infected human (curative) and its' impact were graphically observed. The incremental cost effectiveness analysis technique used to determine the most cost effectiveness strategy and we observe that combination of chicken vaccination and human education campaign strategy is the best strategy to implement in limited resources. Therefore, ND can be controlled if the farmers will apply chicken vaccination properly and well in time. ARTICLE HISTORY

The outbreak of COVID-19 was first experienced in Wuhan City, China, during December 2019 before it rapidly spread over globally. This paper has proposed a mathematical model for studying its transmission dynamics in the presence of face mask wearing and hospitalization services of human population in Tanzania. Disease-free and endemic equilibria were determined and subsequently their local and global stabilities were carried out. The trace-determinant approach was used in the local stability of disease-free equilibrium point while Lyapunov function technique was used to determine the global stability of both disease-free and endemic equilibrium points. Basic reproduction number, R 0 , was determined in which its numerical results revealed that, in the presence of face masks wearing and medication services or hospitalization as preventive measure for its transmission, R 0 = 0.698 while in their absence R 0 = 3.8. This supports its analytical solution that the disease-free equilibrium point E 0 is asymptotically stable whenever R 0 < 1, while endemic equilibrium point E * is globally asymptotically stable for R 0 > 1. Therefore, this paper proves the necessity of face masks wearing and hospitalization services to COVID-19 patients to contain the disease spread to the population.

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