Assessment of past Rift Valley fever outbreak using Modeling, Risk analysis and decision tree in Sudan

A retrospective study was performed in selected states of the Sudan that include Gezira state, White Nile, Blue Nile, Khartoum, River Nile and Sennar states in order to determine the seroprevalence of Rift Valley Fever (RVF) and associated risk factors as well as an attempt was made to apply mapping, risk analysis tool to investigate the disease .Those epidemiological tools were used for purpose of good management strategies and policy makers as well. The source of data was epidemiological reports and archives from the Federal Ministry of Animal resources, universities and Non Governmental Organizations for outbreaks of RVF also and laboratory reports of serum samples tested by ELISA. The test performance characteristics were 99% test sensitivity and 99% test specicity.A total of 3393from, sheep, goats and cattle were sampled and selected to be examined. Estimated Seroprevalence of RVF was 0.15% (n=905) in sheep, 0.20 %( n=776) in goats and 0.13 %( n=638) in cattle respectively. Also information gathered was used to determine the distribution of the disease, transmission and recovery rate of infection over point in time. female and high mortality among young animals and humans. Mosquitoe is the principle vector of the disease. It is transmitted by direct contact with infected tissues or organs of animals and ingestion of uncooked or row milk (1). The study was carried out to investigate the risk related to RVF seroepidemiology and distribution of the disease among livestock and to determine the most ecient policies in management of RVF outbreak by using retrospective data, however more further serosurveillances were required to thoroughly understand the epidemiology of the disease.


Introduction
Rift Valley Fever (RVF) is arthropod-borne viral zoonosis disease. It affects small ruminants, sheep and goats, and large ruminants like cattle and camel, and also can affect human. Rift Valley Fever virus (RVFV) belongs to the family Bunyviridae, genus Phlebovirus. The rst isolation of RVFV was done in Kenya (4).RVFV is a negative sense RNA virus. It is peracute or acute febrile disease that is characterized by numerous abortions in female and high mortality among young animals and humans. Mosquitoe is the principle vector of the disease. It is transmitted by direct contact with infected tissues or organs of animals and ingestion of uncooked or row milk (1).

Objectives
This paper is to understand epidemiology of Rift Valley fever in the study by using Risk analysis tools.

RVF statistical model
Statistical model was analyzed based on data and information given during RVF outbreak. Model for RVF was mathematical or compartment model which referred to S (susceptible), I (infected) and R (recovered) from the study population ( Fig. 1). It is used to investigate the distribution of disease in the population. It has been built on SIR Model template adopted for in uenza virus by (6). The parameters for host and vector models were obtained from literature (5), (15). The study assumed that population was homogenous. The model was comprised from a system of three coupled non-linear differential equations (Tables 1 and 2 Where, Ś is susceptible, Í is infected and Ŕ is recovered or and immunized individuals, β is transmission rate, γ is recovery rate and denote the derivatives with respective to time t. N denotes for population size. If S (0) = S0 < γ ÷ β, both S (t) ant I (t) decreased and converged to a point on the S-axis; There is no outbreak. If S0 > γ ÷ β, I (t) rst increased in the region (γ ÷ β, I) and then decreased to 0; in this instance outbreak occurs. In conclusion, there was a threshold value γ ÷ β. De ne as the basic reproduction number (R0). (1.6) and S0 < γ ÷ β↔R0 < 1, (1.7) If R0 < 1, RVF epidemic dies out, when R0 > 1 a RVF outbreak is possible, (17). The nal model has been calculated by disease-euler-quad model which as follow R0*= r (n) + ((1-d)*r*I (n))*C + 0.5((1-d)*r*(k*S (n)*I (n)-r*I (n)))*C^2 (1.7)

SIR Model in host
A total of 50000 hosts were entered in SIR model over time, to explain the trend of the disease. Population structure was 58.8% susceptible, 3.9% infected and 37.3% recovered. The model was found that at 0.18% of the herd seroprevalence of sheep ocks has shown only one positive case could be detected in order to consider that the herd was positive for RVF, While at 0.56% herd seroprevalence of goat ocks only one positive case could be detected in order to consider that the herd was positive for RVF and at 0.73% herd seroprevalence of cattle only one positive case could be detected in order to consider the herd was positive for Rift Valley Fever (Figs. 2,3 and 4).
A 0.12% of cattle populations were enforced in the model. The adjustable parameters for the nal model were 49990 susceptible, 10 infected for 50,000 animal hosts, 0.000004 was transmission rate, 0.021918 was recovery rate and 0.3 death rate. The curve of susceptible population were declining at 500000, curve for infected were increasing and reached the peak at 30500, while recovered had gotten plateau at 40000 (Fig. 2).The sheep populations were 50390000, and the goat populations were 42756000 with density of 20.11 and 17.06 respectively. A 0.1and 0.12% from sheep and goats were entered in RVF Model, respectively. The parameters were a susceptible (S0), 49990susceptible, 10 infected for50000, 0.000004 transmission rates, 0.02 recovery rates and 0.03 death rates. The curve for susceptible sheep and goat were declining at 30500, curve for infected were reached 20500, whereas recover get plateau at 50000 (Fig. 3and 4).

Vector model
This study had revealed that Mosquito as a principle vector to transmit RVF in the Sudan, Aedes spp was a primary vector to cause RVF according to its biology which renders RVFV to survive for longer period during dry season in Dambos "land depression". This feature (transovarian transmission) was to preserve RVFV in mosquito's egg; when ooding comes, infected eggs hatch and are up and disseminate RVFV to susceptible population depending on mosquitoes vector density. Culexs pp has found to have a secondary role in transmission of RVFV in the Study area from 1973 to 2007 (Table 2).
A total of 60000 sample of mosquitoes were entered in SIR model after pooling with 95% con dence limit (CL), transmission rate was 0.000005, death rate was 63.8% and RVF recovery rate of mosquito was 0.02 ( Fig. 5), (Table 4).
Vector Model is referred to suspected (s) is decreasing at 30 individual, infected(I) was increasing at 50 individual and recovered (R) was increasing at 95 individual with 100 time iteration. This was development of epidemic curve in vector at a point in time. This to explain distribution of RVFV in mosquitoe vector population by dividing it into three parts.  (Fig. 7).

Discussion
In this study, SIR Model had analyzed dynamic and epidemiology of RVF in study population. The populations at risk were estimated over 30,000 heads for sheep, goat and cattle, whereas study host was more exposed to RVFV (Fig. 2,3and 4), with uncertainty analysis that ranges from 0.01 to 610.65, with con dence of 95%, although there is lack of information and data available for the disease during study, which is important to know the dynamics of the disease when it occurs. Clustering had been reported in Gizera state, where foci or pockets of the disease were present; this had come into agreement with research done by (8), where clustering can estimate the incidence of RVF in study area for a certain period of time which provides understanding for the spatial distribution and epidemiology of RVF. Frequency of annual temperature and annual rain fall were been analyzed to understand its relatioship with RVF outbreaks in study area.Environmental risk factors like ElNioSouthern Oscilliation, Average Annual precipitation and Elevation Map had signi cant and important role to play as predisposing factors to occurrence of RVF by increasing of rainfall which improve multiplication of RVF insect vectors to dissemenate the virus to susceptible hosts. Studying the climate and ecosystem, RVF was found to be correlated with weather anamolies and Elino phenomenon in Eastern Africa by (22), which was leading to up-average rainfalls that prefer replication and increased mosquito density. This has important role in tramission cycle of RVFV to exposed host, when the virus can survive in egg of pregnant mosquites which could be dormant in dambos or land depression for long peroid of time specially in interepidemic peroid and when rainfall come, it ared up and dissmenated the virus to suspected hosts, this is has been signi cantly important observation in East of Africa. Also, it had explained that parameters of deterministic models ( 2) is analyzing the multiplication rate of the disease and rate of infection in a given geographical zone .Vector model had analyzed more than 80% of mosquito to carry RVFV to the vector, given that susceptible hosts were exposed to the vector, RVF outbreak is likely to occur with 95% con dence. In addition, entomological survey had shown that Aedes vexans and Culex quinquefasciatus were positive to RVF virus (13).Therefore, epidemiological model for RVF in this study was carried out analysis of SIR model, vector model, spatial mapping model and risk factors associated with RVF seroprevalence. Epidemiological model for this study had manifested probability distribution of RVF on study population and different degree of statistical differences and association for host population, environmental risk factors with RVF seroprevalence, this agreed with the effect of environmental risk factors and disease dynamics on population by (23), whereas models is build up on availability of information and report about the disease; Although it is also important to improve the knowledge about disease by analyzing available information by using disease models. RVF is mainly endemic in Africa and these are involving several regions and countries in the same time. Also, it had occurred outside African continent in Arabian Peninsula and some Indian Ocean islands. It was associated with periodic cycle and heavy rain falls and ooding which usually occurred after interval which prefers mosquito proliferation. RVFV was rst reported in Sub-Saharan Africa and southern Africa (3).Although the virus had been found outside Sub-Saharan Africa to Egypt (Gerdes,2004), Saudi Arabia and Yemen (24). In 1973, RVF outbreak was erupted in Southern Africa where human deaths were reported (12). A 958 human causalities in1977 and 200 human deaths in 1978 were occurred due RVF epidemic in Egypt. In Kenya and Somalia, RVF caused 478 human deaths in 1997 (14). In 2000, RVF outbreak was con rmed in Saudi Arabia and Yemen with 882 con rmed cases and 124 deaths (11). In the Sudan, serological evidence of RVF was reported in 1936 which revealed 6.7% of 164 human sera by using precipitating antibodies (7). In addition, reporting of cases of RVF, diagnosis and treatment capability and raising awareness of the disease epidemiology, training of medical cadres and research and development is importantly signi cant to exceed the planning and policy to contingency and preparedness against RVF and reducing its spreading in suspected countries.

Conclusion
Rift Valley Fever (RVF) is arthropod-borne viral zoonosis disease. It affects small ruminants, sheep and goats, and large ruminants like cattle and camel, and also can affect human. Rift Valley Fever virus (RVFV) belongs to the family Bunyviridae, genus Phlebovirus. The rst isolation of RVFV was done in Kenya (4). RVFV is a negative sense RNA virus. RVFV genome is structured from three partites, small, medium and large. It is peracute or acute febrile disease that is characterized by numerous abortions in female and high mortality among young animals and humans. Mosquitoe is the principle vector of the disease. It is transmitted by direct contact with infected tissues or organs of animals and ingestion of uncooked or row milk (1). The study was carried out to investigate the risk related to RVF seroepidemiology and distribution of the disease among livestock and to determine the most e cient policies in management of RVF outbreak by using retrospective data, however more further serosurveillances were required to thoroughly understand the epidemiology of the disease.       Uncertainty analysis for SIR model. Uncertainty was obtained by estimating the standard error (SE) of sample (SE mean was 26.6 for suspected, 139.3 for rate of contact and 0.15 for duration of infectionness) with 95% con dence interval. It was measuring the degree of goodness of t for the model with optimization of assumed parameters to be simulated at SIR model. This analysis is to investigate the accuracy of disease model that has be studies in this research.