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Cholera is a bacterial disease caused by the bacterium Vibrio cholerae that requires optimal temperature and environmental conditions to survive. It is well known that climate change, influence of ecology, flood and droughts can affect the concentration of the bacterium in the environment. The goal of this article is to establish the effects of hygiene, famine, climate and environment on the transmission and spread of cholera. The transmission dynamics of the disease are modeled with a non-autonomous system of ordinary differential equations that is coupled to a model of intra-annual variation of Vibrio cholerae in the environment. When the intra-annual variation of Vibrio cholerae is not incorporated into the model, this latter becomes autonomous and we then give an explicit formulation of the basic reproductive number. In the non-autonomous case, we make analytically explicit two thresholds that allow to exhibit cases where disease extinction otherwise disease uniform persistence may occur. Finally, some numerical simulations allow to study the evolution of the cholera spread according the different environmental factors.The principal factors of outbreaks and spread of cholera are favorable in Africa. Severe outbreaks of cholera have been directly associated with flood and war [18,39]. The famine caused by war is also a parameter in Africa, because gastric acid failure is favorable to the spread of Vibrio cholerae [4,14,18,39].Many studies have focused on the association between weather factors and occurence of V. cholerae. Particulary, the relationship between the occurence of V. cholerae, temperature and salinity (measure of parts salt per thousand parts seawater(ppt)) were investigated. [7,8,15,18]. The most favorable salinity for V. cholerae is between 2 and 14 ppt, and the optimal salinity appeared to be between 2 and 8 ppt. The most favorable temperature is between 10 • C and 43 • C, the optimal temperature appeared at 37 • C [7, 8].However, there are studies that have investigated the relationship between the occurence of V. cholerae, river levels and vegetables. The pH of specific vegetables and water is an important factor that influences contamination by V. cholerae. The most favorable pH is between 5 and 10 with the optimal pH of contamination at 8 [4,18,22].The spread of disease is then influenced by the environment, weather factors and socioeconomic status. Thus, to study the dynamics of the transmission, it is important to take into account the following factors: climate (temperature and rainfall), environment (pollution, vegetation and proximity of lakes or rivers) and education of the population [18,22,26,39,41].Several kinds of mathematical models have been proposed to understand the dynamics of transmission of cholera, mainly described by SIR models, where are incorporated the effect of temporary immunity and a distinction between asymptomatic infected and symptomatic infected [9,11,42]. The direct and indirect transmission both have been considered in the previous models. The hyperinfectivity...

Climate change influences more and more of our activities. These changes led to environmental changes which has in turn affected the spatial and temporal distribution of the incidence of vector-borne diseases. To establish the impact of climate on contact rate of vector-borne diseases, we examine the variation of prevalence of diseases according to season. In this paper, the goal is to establish that the basic reproductive number [Formula: see text] depends on the duration of transmission period and the date of the first conta-mination case that was declared ([Formula: see text]) in the specific case of malaria. We described the dynamics of transmission of malaria by using non-autonomous differential equations. We analyzed the stability of endemic equilibrium (EE) and disease-free equilibrium (DFE). We prove that the persistence of disease depends on minimum and maximum values of contact rate of vector-borne diseases.

In December 2019, human cases of novel coronavirus infection were detected in Wuhan, China which have been named as COVID-19 by the World Health Organization (WHO). Since COVID-19 was first detected in China, the virus has reached more than 120 countries and was declared a global pandemic on March 11, 2020 by the WHO. In this paper, we have highlighted the influence of temperature on the spread of COVID-19. For this, the dynamic transmission of COVID-19 is modeled taking into account the influence of the temperature on the persistence of coronavirus in the environment. We also took into account the impact of proportion of people who respect the barrier measures published by the WHO on the scale of the COVID-19 pandemic. Taking into account the influence of the temperature on the persistence of the virus in the environment, the dynamic transmission has been described by a system of ordinary differential equations (ODEs). First, we analyzed the solutions of system in the case where the impact of the temperature on the virus is neglected. Second, we carried out the mathematical analysis of the solutions of the system in the non-autonomous case. Mathematical analyzes have enabled us to establish that the temperature and proportion of persons who respect the barrier rules can affect the spread of COVID-19. Some numerical simulations have been proposed to illustrate the behavior of the pandemic in some countries.