Globally, the COVID-19 presents a serious concern to the wellbeing of people. COVID-19 was first detected in Wuhan, China. The disease became a source of concern for Nigerians after the country registered its first case in February 2020. Currently, the country has recorded 255,103 confirmed cases, 249,246 recovered cases, and 3,142 deaths as of March 21, 2022. We proposed a SEQIHRV model to investigate the spread of coronavirus disease in Nigeria. This model defines the infection dynamics' transmission routes as well as effect of contaminated surfaces on the human population. Unfortunately, the virus's propagation and mortality from COVID-19 is increasing daily. Therefore, it is required to manage and control the flow of the infection. The impact of control measures as time-dependent interventions was investigated in this study utilizing optimization technique to determine their effects on the spread of Corona virus. The basic reproduction was calculated and used to calcite the sensit.....

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We proposed and analyzed a nonlinear mathematical model for typhoid fever and optimal control in a community with overpopulation. The model considered the effect of environmental precautions on the transmission of typhoid fever. We obtained the basic reproduction number denoting the epidemic indicator. We proved the local and global asymptomatic stability conditions for disease-free and endemic equilibrium. The model exhibits strategies for optimal control of typhoid fever, such as preventive strategies (environmental sanitation, proper hygiene, vaccination) and the treatment strategy. The numerical simulation of typhoid fever disease transmission and its maximum control summarized that prevention and treatment are the best methods for eradicating the disease in society. Since 0.1174, R0 _ which is less than one, it follows that the disease-free equilibrium is asymptomatically stable, and that the disease will always die out. Keywords: Mathematical model; Basic reproduction number, Di.....

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